Slashdot Mirror
Making Change
Roland Piquepaille writes "There are mostly four kinds of coins in circulation in the U.S: 1 cent, 5 cents, 10 cents, and 25 cents. But is it the most efficient way to give back change? This Science News article says that a computer scientist has found an answer. "For the current four-denomination system, [Jeffrey Shallit of the University of Waterloo] found that, on average, a change-maker must return 4.70 coins with every transaction. He discovered two sets of four denominations that minimize the transaction cost. The combination of 1 cent, 5 cents, 18 cents, and 25 cents requires only 3.89 coins in change per transaction, as does the combination of 1 cent, 5 cents, 18 cents, and 29 cents." He also found that change could be done more efficiently in Canada with the introduction of an 83-cent coin and in Europe with the addition of a 1.33- or 1.37-Euro coin. Check this column for more details and references." The paper (postscript) is online.
I think the advantage to having a 10-cent piece is that it makes the math easy. Let's face it; can you imagine the average cashier at WalMart giving back 98 cents change with an 18-cent coin?
Swannie
:q!
More and more transactions are done electronically. Does anybody really want to go back to shilling, farthings, etc etc?
Trolling is a art,
Are you kidding me?!
... *pause* .... and just stare blankly at the change drawer.
Have you ever gotten a bill for dinner for say $12.50 and you give the cashier $15 saying the tip is included?
You would think 15.00 - 12.50 is doable right?
HELL NO! The cashier pulls out a calculator to do the math so she can write it in for the waiter's tips!!!
If people can't add things like this 18cent coins are out of the question.
Although I would like to hear a cashier go,
"That makes $0.88 change sir." Pick out two quarters then,
"Engineers do the work of man, Physicists do the work of God"
Is it too early in the morning or does this article not make sense? I have never seen an 18 cent piece in circulation n the US...
Eric Aitala
www.f1m.com
Tell me more about these 18 cent coins!
Why not just get rid of silly prices like 99.99 and 4.37 and 1.49. ?
Why not round prices to dimes ? Or even quarters ?
for the last time people, I am "frodo from middle eaRTH", not "middle eaST".
"There are mostly four kinds of coins in circulation in the U.S: 1 cent, 5 cents, 18 cents, and 25 cents"
Where is this 18 cent coin? Have I been living under a rock? Are my dimes now worth 18 cents?
Everyone is entitled to their own opinion. It's just that yours is stupid.
I had 18 cents everytime I heard that.
I don't suffer from insanity, I enjoy every minute of it.
I was at a conveinece store yesterday. The price came to $1.37. I tendered $2.12. The cashier's head almost exploded.
Here in Canada the only chance of our coinage being worth 87 cents is if the US keeps up it's foreign policy for another 6 months. (our dollar hasn't been this high in about 7 years)
I went to battle MC Escher but drew a blank
Currently in circulation? Must be a collectors item. I would pay more than the fact value for a coin like that!
SPAM solution made easy: 1 spammer, 5 cords of rope, 5 hourses, and fireworks. Be creative.
...to take the ferry costs a nickel. And in those days nickels had pictures of Bumble Bees on them. `Gimme five bees for a quarter' you'd say.
I'll be deep in the cold, cold ground before I recognize the eighteen cent coin.
I don't want to be here.
I hereby declare any future posts mentioning the "18" typo redundant, including this one. Please mod accordingly.
Patrick Doyle
I mod down every jackass who puts his moderation policy in his sig. Oh, wait a sec....
Sorry, but the average white-bread eating American does not have the mental capacity to use an 18 or 32 coin.
It's nice to know, however, that the University of Waterloo math department doesn't do drug testing of their employees.
There is no way that as a cashier, I could *ever* come up with change involving 18 cent coins. This is not because I am math-ignorant, it's just not easy. I mean, come on! There are really and literally people I work with that misfile names alphabetically. They spell "Customer" "Coustomer." 18 cents wouldnt work.
Obligatory weak joke: "Doctor doctor, I've turned into a coin!" "Well that makes a change!" Ho ho, and indeed, ho P
Shallit assumed that every amount of change between 0 and 99 cents is equally likely. Why do I feel like from there on it doesn't worth reading it??????????
1. No sig. 2. ???? 3. Profit!!!
So- you have 7 18-cent coins, Susie gives you 13, and you give Bobbie 3. How many nickels must Daddy give you for your 18-cent coins...?
Then, you get on a train in Boston traveling east at 300 MPH. In 30 minutes, will you really care about how many 18-cent coins you're carrying?
Whew! This water sure is cold!
The Federal Treasury will be announcing new $30.00 bills to replace the old $27.00 bills ..
More proof of the ungoing schism between science and common sense.
Me, I'm on the side of science.
18 cents may give you less coins but it would take more time for a cashier to give you correct change.
Wouldn't local sales tax and price distribution play a major role in usefule coin calculation? While the average may point to an 18 cent coin, the distribution plays a much more important role. Factor in the difference in region sales taxes and you end up with a coin that is not only based-10 friendly, but also fails to meet the intended results.
Then again, maybe I should RTFA. Then again, this is
All your base are belong to us!
You think it's bad enough when the cashier has to use the machine to figure out how much change to give, and in what denominations? You think it's bad when the little old lady in front of you in line starts counting, and then double-counting to make sure, the change she's going to hand over?
You give them a 29 cent piece and see how fast things get.
I'm willing to bet that most of the "coin cost" or whatever you want to call it comes from pennies, anyway -- if the dollar amounts are random, every 5 transactions are going to involve (0 + 1 + 2 + 3 + 4 = ) 10 pennies, or 2 pennies per transaction. Rounding prices to the nickel would be simpler, easier, and more efficient.
employee theft. .99, or 1.95, or 7.53, they gotta make change by opening the register.
If the price is 1.00$, the person working the regster can just take the buck, or five, or whatever, and slide it into their pocket. If its
All Troll + "offtopic" mods are meta moderated as "Unfair", because you abused the system.
more efficient transaction costs?? Again the computer scientists are concentrating on the efficiency of the system, without any regard to the efficiency of the user. What is more important, handing back a smaller amount of change, or allowing for quicker mental computation of what coins to use in the transaction? For example when you are told something costs $3.48, it takes more time to calculate how to break up 48 cents into the available coin denominations, then it does to to actually exchange and identify the coins. The system is not what needs to be optimized, instead the user is what matters, and our mind work well in 10's and 5's.
My mother went to the store to purchase something. The price on it was $20. It was also marked 25% off. It rang up as $18 instead of $15. My mother pointed this out, but the cashier would have none of it. "No, no, that sounds like 25% off."
How the hell can we expect these people to handle 18 cent pieces when they can't even figure out what 25% of 20 is?
The actual solution to eliminating time wasting change is this
instead of $9.99 plus tax, charge $10 plus tax, in Canada tax is 15%, so it would be $11.50, nice and even. Round up all those fuckin' $9.95, 14.95, $39.94, $199.95 and such prices UP, yes, UP, round them to the nearest 5 or 10. Simple.
What the fuck kinda mathematician doesn't consider the logic of the world before embarking on studying it?
18 cents? Holy living fuck, I'm starting to think that all of these errors in Slashdot stories are purely intentional. How in the hell can you let something like that slip through? I can't even begin to imagine. Do people even *read* submissions before they get posted?
Using base 2, with 1 cent, 2 cents, 4 cents, 8 cents pieces, ..., $1.28 bills, ...
you actually can have any amount up to $10245.76 using a maximum of 20 pieces/bills.
On average you'd have 10 pieces/bills, which is not too bad.
To have 20 dollars bills and "round" amounts is irrelevant: taxes always cast the amount you have to pay into a float anyway.
So we are spending our hard earned dollars to fund a research on how to give change back.
They are making real progress in improving mandkind... maybe one day we'll get this magic coin that can represent everything under 10 cents...
Do what Australia did a while back and round everything to the nearest 5c and get rid of 1c and 2c coins entirely (so now Australian coins are 5c, 10c, 20c, 50c, $1 and $2). I couldn't decide whether I liked it to start with, but after a little while you realise just how much shrapnel you carry around and have no intention of using except to empty it from your pocket/wallet at the end of every day. Every time I go to another country and have to again deal with 1/2 cent/euro cent/pence/etc I just appreciate this move even more.
"Because it's there." - George Mallory, when asked why he wanted to climb Mt Everest, March 18, 1923 (New York Times)
so the pimple-faced cashier at my local taco bell will now spend 20 minutes staring blankly at the register rather than the 15 minutes he currently spends on this activity.
Efficiency is great but give me a hot gordita anyday
Just as irrigation is the lifeblood of the Southwest, lifeblood is the soup of cannibals. -- Jack Handy
This is the real reason they killed off all the dime stores in the US! It was a conspiracy all along! Run away, run away!
-Twilight1In Canada, it's Illegal to pay for any good or service, with more than 25 of any given denomination.
For example, my friend tried to pay his parking ticket with a giant glass jar of pennies. The Clerk took the pennies, kept them and informed my friend that his fine was still outstanding. If the Pennies had been rolled, it would be legal for him to pay up to 25 rolls. As such, he got screwed out of his pennies, and still had to pay the ticket.
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Seriously, though, short of going to the Euro 1,2,5,10,... system we need a smaller 50 cent piece that actually gets used. And, of course, having sales tax already in the items and then priced to the nearest 5 cents would help. I spent 4 or 5 days in Paris before I ever needed or received a 1 or 2 cent euro coin.
Why do we still have pennies anyway? Nobody likes them. They are trying to outlaw them in tollbooths here in Illinois, so even the state doesn't want them. The "leave a penny" containers always seem full where I shop. They are just an annoyance, IMO.
My beliefs do not require that you agree with them.
I only have one thing to say to this: PREVIEW!
Honk if you're horny.
Despite the earnestness of the article and research, this should probably be under Laugh, It's Funny. People grab a calculator for 6 times 3. Imagine having to carry the one for all your transactions?
The fact that other countries with a decimal system of currency have different suggested value coins indicates the "efficient coin" is based on the current economy.
penny, nickel, dime, decoct, quarter,.... The kids are going to have a field-day with this one!
These 18 cent coins are a rare find indeed! There arent many around... But if you look hard enough you will find them.
Ok joking aside... I think he meant to type 10... but he did it more than once.... so who knows.. anything is possible I guess...
Here on planet earth, many of the clerks I deal with have trouble counting out change with the current denominations. If they have trouble counting by fives, how well do you thing they'll handle counting by 18 or 29.
This is a classic computer science problem: the guy optimized space over time.
:)
He came up with a solution that presents the fewest coins -- that is, the most "compact" solution in space, where space is number of coins. However, this solution comes at the cost of computational complexity -- the time required to figure out the math.
It's an interesting notion, and worth considering, but in practice it's not viable. I value my TIME far more than I value the SPACE in my change purse.
While these demoniations may be more efficent for reducing the number of coins per transaction, I would think that they would increase the complexity of the math requuired to do the transaction, and the time to count the change back.
This would not necessairly increase the efficency of change transactions.
I would think the implementation of the "Two Penny Lottery" would reduce the amount of change needed just nicely.
Pennies would be removed from circulation, although for electronic transactions, everything would still be counted down to the nearest cent.
If the pack of gum I just bought comes to $0.88 (with tax) I would pay $0.90 and loose two cents. Things would even out because I would come out ahead by paying only $0.85 if it cost $0.87
That would reduce the number of coins less than a dollar in circulation to three.
This is the worst idea ever. Has this person ever been out of the math department?
A much better idea - round to the nearest 10 cents!
Why, that's as queer as a $3 bill!
Bill Clinton: Pimp we can believe in. - The Shirt!!!
Or in this case, that the 0 was an 8 -- repeatedly :-)
DO NOT LEAVE IT IS NOT REAL
1.37 cent??? Is this man completely fakakte?
;)
People already got used to the euro and are calculating it's value in their old currency every time they have to handle prices. I've heard that certain elderly french people even convert the euro prices to old france, a currency that expired decades ago. If you add to that such superodd values, you can expect total chaos throughout of europe - except perhaps for germany, where the exchange rate between DM and Euro is almost 2:1
If a train station is a place where a train stops, what's a workstation?
There's no way you're going to teach entire countries to just op thinking in terms of 1, 5, 10, 25 and start thinking about 83 cent coins, or 1.37 dollar bills... The effiency achieved would most likely take years to just balance the inconvenience and trouble caused by shifting the way money has worked in the past. It wasn't too many years ago that I worked at a grocery store, and I can still tell you all the finer points of a change drawer (i.e. one of each coin makes 41 cents). Too many people rely on the situation not changing.
"Shallit assumed that every amount of change between 0 and 99 cents is equally likely."
Most things I buy are xxx.99 or xx.29 or xxx.50 or xxx.00 etc. so (extrapolating to the general public) I would say the average change amount required for change-requiring transactions is *not* an even distribution.
The article says he assumed all amounts of change between 1 and 99 cents have the same probability. I would argue this is not true - how many things are $X.99 plus tax, or similar?
This looks like yet another "It works on paper" idea. It should be a requirement for these guys to leave the lab once in a while.
The difference between theory and practice is: in theory, there should be no difference between theory and practice. But in practice, there is a big difference.
Anonymous Kev
proudly posting as AC since 1997
It seems like the objective here was to minimize coin exchange. Ususally I try to minimize the number of coins in my pocket.
If something costs 77c I give them 1.02 - and get a quarter back. In the US, the tellers stare at me blankly, but then dutifylly enter the amount I give them - and then smile in amazement at the simplicity of the exchange.
In Japan, it is almost the other way around. The tellers come up with the most creative combinations that minimize my number of coins (and maximize theirs - this is in both of our interest).
Tor
what about asking these fscking marketers to drop their psychological price philosophy and sell things for 1$ instead of 99 cents ???
Trolling using another account since 2005.
If there's any mistakes, you should have used the preview button!
Apparently, we have different rules than they.
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- Some egghead thinks "optimal" means "fewest coins returned in change, on average."
- He recommends introducing 18 and 83 cent coins.
- The people who actually use coins laugh at this idiocy.
Sheesh, "optimal" coinage denominations are those that make using coins easiest. That means quick mental calculations of change, manipulating them with your fingers, and passing them back and forth.The ivory tower academics are certainly earning their reputation for foolishness.
taken! (by Davidleeroth) Thanks Bingo Foo!
Love the idea.
My math: 4.70 - (0+1+2+3+4)/5 = 2.70 (Probably close but wrong)
'SBEMAIL!' is better than a goat!!
Get rid of any coins which are too small to actually buy anything with. That way you don't wind up having to periodically pick through your small change to get rid of those 1 and 2 cent pieces which you only have because everythings priced at xx.99 or xx.98.
If I seem short sighted, it is because I stand on the shoulders of midgets
When I travelled to Australia a few years back they had just finished doing this. They only time they really had to round anything at the register was in the case of things like produce where you weigh it and could come up with odd values. Sales tax wasn't a problem either, because they had value added tax.
"Tolerance is the virtue of the man without convictions." -- G. K. Chesterton
Any gain in efficiency of number of coins returned is going to be substantially offset by the decrease in efficiency of time required for people to calculate the change. Seriously, the simplest solution is to do away with the penny and round up/down to the nearest nickel.
"Nothing exists except atoms and empty space; everything else is opinion." - Democritus
After about 10 transactions, rounding to the nearest dime every time would be basically fair for everyone involved, given that you will round down as often as up... and would mean we'd only need 10c, 20c, and 50c coins.
I have a scheme that guarantees only one coin is returned in change for any transaction.
taken! (by Davidleeroth) Thanks Bingo Foo!
at least with 18 cent coins, i'll be able to sympathize with the till-monkey who's struggling to make change for me...
Having...flashbacks...discrete math...AAAAHHH! :)
I remember having a discussion in class about this. We just came to the conclusion that most people are too lazy or stupid to figure out anything other than multiples of 5 and a few pennies. The professor agreed and we moved on to the next topic
Sometimes I doubt your commitment to Sparkle Motion.
Microsoft hires so many grads from the University of Waterloo...
Let me guess... the 18 cent piece only works in vending machines and cash registers running the Windows operating system.
You will have to pry my proprietary software $$$ from my cold dead hands!
Don't y'all remember the SchoolHouse Rock about counting by 18?
. . .
*taps foot*
Eighteen is a magic number.
Yes it is, it's a magic number.
Somewhere in the ancient, mystic eighteenity
You get eighteen as a magic number.
The past and the present and the future,
Faith and hope and charity,
The heart and the brain and the body
Give you eighteen.
That's a magic number.
18, 36, 54 . .
72, 90, 108 . .
126, 144, 162 . .
180.
So, if we implement this, we'd receive fewer coins in change. So? We'd still just take them home and dump them into the Spare Change Jar, where they'd lie cloistered until the next poker night. What problem did we solve?
Oh, yeah, it's not easy to pad these out to 120 characters.
this is the stupidest thing ever. the reason we have 1, 5, 10, and 25 cent coins is because the math is easier. plain and simple. if someone owes $4.74 cents, we know how to split that up easily into several combinations of pennies nickels dimes or quarters. what if we used 18 cent coins? this guy wasted how much time (=money) doing this study??
This approach simplifies all transactions to one-coin change. Some people might argue that this is just too many coins to keep track of, but since no one keeps track of their change anyway, it wouldn't matter. It's easier to use the new change to pay as well: Instead of $0.67 being 2 quarters, a dime, a nickel, and 2 pennies, it can be paid in one coin. Or, you could use a 50-cent and a 17-cent piece. Or two 27s and a 13! The possibilities are endlessly easy!
Some people say that it's a problem to differentiate the 99 different coins (95 new coins) by sight. There's a simple answer to this -- each coin would have a number of sides based on its amount. A 4-cent coin is a square, an 8-cent is an octogon, and so forth. So, remember, don't give them three quarters -- just reach into your pocket, feel for the coin with 75 sides, and hand it over.
Oh, and if you can't tell a 99-sided coin from a 97-sided coin by sight, perhaps you should stick to smaller denominations.
The new two-cent coins are easy to lose, so be careful.
/syle
Life would be so much easier if we just switched to quatloos.
_ _ _ Go for the eyes Boo! GO FOR THE EYES!
scientist: "i have found a way to make men attract more women...all they need to do is apply newton's second law by differentiating against the chaos theory multiple and apply some basic intertia formula. problem solved, so now i'm investigating a better mechanism to take a piss deriving from fermat's last problem"
So I go throught the Taco Bell drive-through, and my total was $3.51. So to avoid getting back 49 cents in change, I give the cashier $4.01. The girl gives me 49 cents change. Rather than argue the point I just drove on. If people can't handle an extra cent, how are they going to handle an 18 cent piece? That requires, like, math and stuff.
But my thoughts were to reduce the number of different coins. Instead of 1-2-5 in each decade, how about only 1-3?
The introduction of an 18-cent coin does not really make sense, because, as described in the article, people mostly use the "greedy algorithm" to calculate change.
The 18-cent coin (or the 1.33 Euro-coin or whatsoever) would only make sense if the denominations of coins given as change were to be determined by a computer, which in 99% of all situations is not the case.
I think cashiers would nearly always use 18-cent coins together with 2 pennies because it is easier to do the math with multiples of five.
where's all that Karma?
I've always thought the Americann system of coins was far inferior to the British system. For one thing, you have to give a name to every damn coin that you produce, making it hard to know how much one coin is worth if you're a foreigner (I still don't know, is a nickel 5 cents? 10 cents???) In the UK we call our coins 1p, 2p, 5p, 10p, 20p and 50p. Nice and easy.
For second, you've got the idiotic 'quarter'. 25 cents is NOT a sensible sum of money to be carrying around, as it is not rounded to 10. Any coin worth more than 1/10th of a dollar should be rounded to the nearest 10.
Also, you don't have a 1/2 dollar coin. Why not?
== Jez ==
Do you miss Firefox? Try Pale Moon.
I thought this was one of the most basic problems of linear optimization?!? I remember discussing this same problem with fellow students within the first few weeks of my linear optimization class. This was something they figured out in the 70's or something. I never paid much attention to the history aspect :shrug: Theoretically, it would make sense to make changes to the monetary denominations in order to make transactions more efficient and thus boost productivity.
However, the changes would not work in practical terms today because logistics involved in removing the affected coins from circulation. Think about all the vending machines and cash registers out there!
Rangers Lead the Way!
As I recall from Algorithms, the greedy method (always take biggest coin) is optimal for our 1-5-10-25 system. Would this mess that up, forcing us to revert to dynamic programming? Screw adding 18 cents, I think cashiers real problem will be DP.
This is not a signature.
Well that confused the hell out of me.
I do security
LAME ARTICLE ...
(thats my 2 cents)
In finding coin denominations that minimize the average cost of making change, Shallit assumed that every amount of change between 0 and 99 cents is equally likely.
I think that this is not the case. Currently, many prices are tailored to avoid the use of pennies. How many vending machines, for instance, will even accept pennies? If this is a significant effect, his "optimization" is going to be seriously flawed.
Floating face-down in a river of regret...and thoughts of you...
How much money was spent on this?
I hope
Ancker
Marge: I'm Marge Simpson, and I have an idea.
Everyone: Aw, no. Marge is going to say something. etc.
Marge: Now, I know you haven't liked some of my past suggestions,
like switching to the 18 cent piece--
Abe: [stammers a little] The 18 cent piece is the tool of the
devil! My car gets forty rods to the hogshead and that's the
way I likes it.
Quimby: The old person's remarks will be stricken from the record.
Abe: Who said that?
[2F31]
M@
Krispy Cream is people
Why did we fight against the Imperial System ?
:
easy, look
Measures of length
After 1959, the U.S. and the British inch were defined identically for scientific work and were identical in commercial usage (however, the U.S. retained the slightly different survey inch for specialized surveying purposes). A similar situation existed for the U.S. and the British mass unit pound, and many relationships, such as 12 inches = 1 foot, 3 feet = 1 yard, and 1760 yards = 1 international mile, were the same in both countries; but there were some very important differences.
Measures of volume
In the first place, the U.S. customary bushel and the U.S. gallon, and their subdivisions differed from the corresponding British Imperial units. Also the British ton is 2240 pounds, whereas the ton generally used in the United States is the short ton of 2000 pounds. The American colonists adopted the English wine gallon of 231 cubic inches. The English of that period used this wine gallon and they also had another gallon, the ale gallon of 282 cubic inches. In 1824, the British abandoned these two gallons when they adopted the British Imperial gallon, which they defined as the volume of 10 pounds of water, at a temperature of 62F, which, by calculation, is equivalent to 277.42 cubic inches. At the same time, they redefined the bushel as 8 gallons.
In the customary British system the units of dry measure are the same as those of liquid measure. In the United States these two are not the same, the gallon and its subdivisions are used in the measurement of liquids; the bushel, with its subdivisions, is used in the measurement of certain dry commodities. The U.S. gallon is divided into four liquid quarts and the U.S. bushel into 32 dry quarts. All the units of capacity or volume mentioned thus far are larger in the customary British system than in the U.S. system. But the British fluid ounce is smaller than the U.S. fluid ounce, because the British quart is divided into 40 fluid ounces whereas the U.S. quart is divided into 32 fluid ounces.
From this we see that in the customary British system an avoirdupois ounce of water at 62F has a volume of one fluid ounce, because 10 pounds is equivalent to 160 avoirdupois ounces, and 1 gallon is equivalent to 4 quarts, or 160 fluid ounces. This convenient relation does not exist in the U.S. system because a U.S. gallon of water at 62F weighs about 8 1/3 pounds, or 133 1/3 avoirdupois ounces, and the U.S. gallon is equivalent to 4 x 32, or 128 fluid ounces.
1 U.S. fluid ounce = 1.041 British fluid ounces
1 British fluid ounce = 0.961 U.S. fluid ounce
1 U.S. gallon = 0.833 British Imperial gallon
1 British Imperial gallon = 1.201 U.S. gallons
Measures of weight and mass
Among other differences between the customary British and the United States measurement systems, we should note that they abolished the use of the troy pound in England January 6, 1879, they retained only the troy ounce and its subdivisions, whereas the troy pound is still legal in the United States, although it is not now greatly used. We can mention again the common use, for body weight, in England of the stone of 14 pounds, this being a unit now unused in the United States, although its influence was shown in the practice until World War II of selling flour by the barrel of 196 pounds (14 stone). In the apothecary system of liquid measure the British add a unit, the fluid scruple, equal to one third of a fluid drachm (spelled dram in the United States) between their minim and their fluid drachm.
In Great Britain, the yard, the avoirdupois pound, the troy pound, and the apothecaries pound are identical with the units of the same names used in the United States. The tables of British linear measure, troy mass, and apothecaries mass are the same as the corresponding United States tables, except for the British spelling "drachm" in the table of apothecaries mass. The table of British avoirdupois mass is the same as the United States table up to 1
It takes 40+ muscles to frown, but only four to extend your arm and bitchslap the motherfucker
I understand that an assumption like this is necessary to even begin an anaylysis using our western logic system, but this assumption makes the study useless.
There's no way that the distibution curve is flat. People spend a lot of time and money price setting as described here and you better believe they know how to price their goods to maximize profit.
This study also doesn't take into account people like me, who make a game out of minimizing the number of coins in my wallet/pocket. If I can prevent getting 94 cents in change by carrying and relinquishing a penny and a nickle, I'll do it.
sHi
In the paper, underneath the section titled "Greedy methods for change-making" the author points out one nice feature of our current system of change, that the optimal number of coins are given when they are given "greedily", that is, as many of the largest denomination are given as possible, then the next largest, then the third largest, and so on.
He points out that this wouldn't be the case in a new system with an 18c coin. For instance, if I owe your 36 cents, The optimal choice would be 2 18 cent coins. However, If I give you change "greedily", you'll get a 25c, 10c, and 1c...3 coins!
The point is that we MUST have a change system with greedily administered change in order for optimality to be relevent. How the hell is a McDonalds clerk going to be expected to solve a non-linear optimization problem each time someone needs change!!!
One can reduce the amount of change simply by getting rid of the silly 1c piece, like Australia did (it got rid of both 1c and 2c pieces).
:)
Sure, people will bitch and moan for about 6 months, but then noone would ever consider going back.
All you need to do is 2/3 round at the till. It's great!
Just cut off one hand of the customer and 50% increase in gloves per human is achived.
Let me guess, this goes along with the rest of computer science. 1024 MB = 1 GB. RAM= 1MB , 2, 4, 8, 16, 32, 64, 128, 256, 512, wtf?>??? I don't care that it doubles, it's retarded. :-P How about 10, 20, 30, 40, people!!
128bit this, 256 byte that. The whole dang system bytes. :-) 8 bits to a byte....oy, my head!
You computer kids, I tell ya. :-P
Freedom Is Universal
Linux-Universe
Having an 18 cent coin or a 29 cent coin will confuse the average person greatly to the point that there will be mistakes on both sides - both for cashiers and for customers. In other words, there could be a greater cost of making mistakes due added marginal losses from incorrect change dispensing and payment than of implementing a system that, at least on the surface, would lead to a raw cost decrease by the numbers.
In other words, applying mathematical optimization can often ignore the real end result when implemented on a wide scale.
He has no taken into account Benford's Law in determining transaction amounts, and is falsely assuming a flat distribution.
Need a Python, C++, Unix, Linux develop
The half dollar is around, but seldom used probably due to the size and weight. If that coin is included in the analysis, what are the results?
This is an interesting exercise, but ultimately impractical. The decimal system of currency was chosen for ease of use. No sense in mucking the user interface to money. After all, look how popular dollar coins, half dollar coins, and two dollar bills are. They're around, but are mainly curiousities, not workhorses of the currency like other denominations.
A binary currency system would also be understandable (after a bit of using it) and would probably have similar inefficiencies.
But let's pretend it's not, and that Jeffrey Shallit is serious. In that case, his error is that he's optimizing the wrong thing. Instead of optimizing the number of coins, think a little bigger, and optimize effort. To a computer that can add and subtract with ease and without error, perhaps that is the same thing. The only effort it experiences is toggling some port to dispense change.
But for humans, the math is effort. 10-cent pieces are better than 18-cent pieces for the same reason that centimeters and liters are better than inches and pints. Even math-literate scientists know better than to measure their car's fuel-efficiency in hogsheads and rods.
Metric money, or more precisely, consistent-radix money, is the Right Thing. Whether the radix is 2 or 10 might merit discussion (I'm a 10 guy, myself).
But 18 and 29 cent coins are a really bad idea. My monkey fingers can mechanically deal out a lot nickles and pennies in the time it takes me to go, "uh...subtracting 18 gets me ... uh .."
As copyright owner of this comment, I authorize everyone to defeat any technological measure which limits access to it.
Also, this would bring us one step closer to utopia, as defined by Star Trek.
Honk if you're horny.
What would that do to the 'queer as a 3-dollar-bill' idiom?
Do YOU want to sit there while a highschool-dropout cashier at McDonalds tries to count your change in $0.83 coins?
Time efficiency or number-of-coins efficiency... gee, which would you prefer? q:]
(No, I didn't read the article, and I'm sure that's discussed, ok?)
MadCow.
I used to have a sig, but I set it free and it never came back.
One thing they're missing is that most people suck at math. Even smart people. Who's going to figure out how many 18-cent coins to give back on a $0.75 "change event"?
I happen to be one of the people all the math geeks are making fun of. I AM the idiot who pulls out a calculator just because I don't trust my sucky arithmetic. I'm just bad at it; always have been, always will be. Round-number coins are the best for quick computation.
efficiency does not come from minimal materials used, it comes from ease of use. who in the world is going to be able to do math with 18, 29, and 83-cent coins?
:-)
If you were moving, would you a) take the time to measure in 3 dimensions and record the size of every object in your house, then order custom-built boxes to exactly fit everything with no extra room, thus using the absolute least amount of cardboard possible, or b) go to MailBoxes Etc and buy twenty 18x18x24 boxes and be done with it? Which is more "efficient"?
As long as I get blank stares for handing the cashier $22 for a $16.85 purchase, this guy's coin scheme is *never* going to fly.
Hell, if they're going to do anything, make a dollar worth $1.28 and use 1, 2, 4, 8, 16, 32, and 64-cent coins. Sure, it might result in more coins being used, but the cashier could just go left to right and pick one or zero coins from each slot in the tray.
Dear Slashdot: next time you want to mess with the site, add a rich-text editor for comments.
What a waste of time and effort. Kind of like those studies that say..."BREAKING NEWS: A recent study has shown that people over 100 have an increased risk of death due to age"...what a waste of resources.
for the 25i cents coin, then I can have virtual cash.
Je t'aime Stéphanie
.. why not just re arange the prices and make the sums average out to a higher number with the taxes, etc? Charging 99 cents and 4.95$ and etc is just silly, I know it's psychological marketing, but it's still doofus, and no one is faked out anymore. Figure it out with that 99 cent thing, drop price to make up for the tax, or round it up, or whatever, but stop with the stupid marketing schemes, then maybe guys like this math whizz could go get a real job someplace instead of studying it. This is beyond busywork, I mean, geeeezzz. Even on big ticket items like cars, you see those obnoxious TV screaming sales guys, selling some car like at 29,999$.
/me, take own advice, go back outside, work on bushhog.
"Wow, see honey, it's a deal, it's only 20 grand and some change!!!"
I mean, really........
ya,ya, I know, it probably keeps working for them though, a sad commentary on the state of education and mass conusmerism brainwashing.
And no, this is one article/paper I slap refuse to read! And I'm going to comment anyway! Somebody go over there and drag that guy outside to go look at pretty girls in the park or something, get him AWAY from the desk. This is obsessive/compulsive behavior on nitro. And I certainly hope he wasn't PAID for that thing.
Just by eliminating the freakin' penny! Since you get an average of 2 pennies back with each cash transaction (NOT 2.5, as (0+1+2+3+4)/5=2), if everybody would just agree to round it to the nearest nickle you would save 1.0 coins. According to his data that gets you to 3.7 cents, which beats his 3.89, avoids having to do base-18 math, and gets rid of those useless pennies in your pocket which are really only good for leaving on train tracks anyway.
Your's for only 9,999 ;-)
:-(
So what we really need....(well in the uk at least) is a 9p 49p and 99p along with the £9 and £99 note.
Then the little barstewards will probably just use ??.98
---
Just because you're paranoid doesn't mean people aren't out to get you
Wouldn't these numbers be affected by inflation? Would governments issue diffrerent denominations every time the value of the dollar/euro/* fluctuates?
This seems like an appropriate time as any to quote the Hitchhiker's Guide to the Galaxy on the subject of coinage:
"The Triganian Pu is a triangular rubber coin, about 3000 km on each side."
Don't blame Durga. I voted for Centauri.
This is the firs cyber problem discussed in the book "Dr Ecco's CyberPuzzles" and collection of problem presented in the column in Dr. Dobbs Journal.
You mean the way they do with gas? Oh, by the way... can you tell me how much you pay in taxes on the gas you put into your vehicle?
It's nice in theory but if they did something like that they could tax you much more than they do now and you wouldn't know.
Summarizing, thats what we'd get. Fewer coins in change but a looooooooonger time for cashiers to figure out how to give it. If someone wants to improve the coining system #change_coins/transaction alone seems like poor criteria. You need to figure out a system that also makes it easy to perform day to day calculations. Maybe even theold british system would be nicer than 29ct coins.
From what I gather in the paper itself, this is more an excercise in optimization and linear algebra than actual viable suggestion.
In the paper itself, the author acknowledges the obvious problem with his analysis: the assumption that prices are equidistributive. He cited two possible sources for non-equidistribution of prices, that of Benford's law and that of the fact that many "labeled" prices we see today ends in the digit "9".
Personally, I don't think Benford's law should play a big influence, at least in the U.S. Since it mostly applies to the leading digit, and I would have a hard time believing that most items sold in the US are priced at $0.1x. In Canada, however, with the smallest bill being 5 dollars, the law might favor purchases of $1.xx over say those with $4.xx.
Also, in regards to the speculation about prices ending in the digit "9", it is well known in analysis that the quantity N*a, where N is an integer and a = p/q irreducible, is equidistributive up to the nearest 1/q. Applying that to the prices, even if the prices have a tendency to end at the digit "9", after the tax, we should consider $0.09 * (1+tax) + some integer * (1+tax)/10 . Which would smooth out the distribution.
Though I speculate that given the current implementation of a sales tax, neither of the author's speculation by themselves would cause a skewed distribution in final amount of change required, we see that combining the two might cause a problem. Since with Branford's law our choice of integer to multiply the tax rate with would not have even distribution, and this might cause a difference. But the analysis is too complicated, and I will leave that for greater minds (or minds not preparing for a final exam) to ponder.
Cheers,
W
Engineers also speak PDE, only in a different dialect.
I don't think an 18 cent coin would be that much of a problem. Any cashier working more than a week developes tricks to count change so not all of them are bad. How many times a day do you think they figure out the best way to give back change from a stock coins that cahnges between customers?
And FYI, Canada is going the other way and introducing a new $5 coin soon. That'll be 1 cent, 5 cent, 10 cent, 25 cent, (50 cent?), $1, $2, $5, and beaver pelt.
Although this seems ideally efficient, in application it probably isnt.
I'm no expert but this reminds me of an asktog.com article where Tog explains how for a person using a microwave to cook something for 1 minute and 11 seconds is faster than setting 1 minute and 10 seconds on the microwave.
Why? Because on the keypad its just easier to type 111 instead of 110 as it takes extra time to move down and find the 0
Similarly (or not), having an 18 cent coin or whatever, is not going to be any more efficient than the current 1, 5, 10, 25 four-coin system.
The extra math is just going to confuse the hell out of people who are used to counting by 5 and 10.
.... ... }
int main (void) {
Once again, yet another person has added fuel to the raging fire that is trivial research. I really hope I'm wrong and some scientist finds a way to feed the world's hungry by applying the time saved by using the eighteen cent piece towards crop production. I know! We'll all save a little energy handling less change, therefore we will consume less resources... "Reduce dependency on foreign oil: use the eighteen cent coin!"
Whatever.
Losers choose to abuse the use of "loose".
Is obviously not true - prices are clustered at certain points, eg 95c or 99c, so the typical amount of change would be skewed as well. Would be nice to see the experiment using real data for typical prices.
Also, I wonder to what extent the demoninations of currency in use effect the prices of goods?
dave
===== Tech, Ramblings, Photos --> davidgoodwin.net
No not that LSD I mean good old pounds shillings and pence. There you have a system which evolved - it sounds to me - to do precisely this. Whats more, even uneducated victorian urchins understood what two guineas less half a crown tuppence ha'penny was and could offer you change in the form of shillings, florins, pennies, etc.
For those who don't know what I'm talking about, British currency up to the 1970s was counted in pennies, shillings (12 pennies), twenty of those to a pound, with a guinea at 21 shillings (lend a pound, get a guinea back in a year, see, works for interest too).
I've read several times that there could be substantial savings from just plain eliminating pennies and rounding to the nearest nickle.
Of couse they could eliminate $1 and $5 bills while they're at it and replace them with coins instead. But even the new Sacajawea dollar is almost never seen, another failure in the US for something sensible. I try to keep merchants aware by getting a roll at the bank every couple of weeks and spending them instead of paper.
But I have yet to see any coin machines that use them. The one machine I'm aware of that dispenses dollar-denominated change still spits out Susan B. Anthony dollars. Even more expensive vending machines at airports (the kind you can get a sandy or something out of) either take sub-$1 coins or bills, no dollar coins.
I think that the premise of this analysis is off. Instead of trying to find an optimal arrangement for change where the minimum is 1 cent, simply eliminate 1 cent coins and make the minimum transaction denomination either 2-cents or 5-cents - that way you have a more limited and more convenient number of possible coin combinations.
I remember that this is how it is done in Switzerland; they have no 1-cent coin - the smallest is a 5-cent coin. This way all transactions are rounded to the nearest 5-cents and it makes the use of change much more easy. The number of combinations of change is much constrained, and its very easy to come up with change quickly and easily. Even a move to a minimum 2-cent coin would improve the situation a lot. Certainly this would be a lot simpler to live with than the ridiculous notion of coins of odd denominations like 83 cents or 1.33 cents.
Mind you, being an amazingly affluent nation of bankers, they have other peculiarities with money also - you could pay for a loaf of bread with a 500 chf note ( bread might cost about 1-3 chf ) and the cashier wouldn't even bat an eye. If you tried to use a 1000chf note they might take a moment to see if its genuine, but they'd still happily make you change for it.
There are a thousand forms of subversion, but few can equal the convenience and immediacy of a cream pie -Noel Godin
Euro 1,2,5,10,
When I was in Europe recently I noticed their semi-log scale change system of 1,2,5,10,20,50,... and really liked it compared with the US system, which has quarter dollars, but not $2.50 bills.
Evidently two bits are indivisible anyway these days, so Americans don't seem inordinately hooked on using powers of 2 to divide up their money all the time.
The US should have its monetary system go the same direction as the stockmarket which recently abolished fractions (down to what, 1/64, 1/128?) in favor of decimal stock prices.
Also, the US treasury needs to push $1 coins (and perhaps $2 and $5 coins) because the paper money wears out so much faster and costs more to replace than coinage.
And, while we're on the subject of monetary redesign, coins should be monotonically increasing in diameter, thickness, and mass to make it easier for people with poor vision.
In fact, if the weights were done nicely, it might even be possible to start weighing heterogeneous buckets of coins to obtain value (assuming no rocks, counterfeits).
Or to measure linear thickness of heterogeneous coin stacks and still have $/inch be as good a measure as $/weight, again, to avoid explicit counting.
Ahh, if nerds were running the world, things would be so damn efficient...
"Provided by the management for your protection."
...In other news today, hot chicks around the world were see smiling, knowing secretly that this guy is never, ever gonna get laid.
"A terrorist is someone who has a bomb but doesn't have an air force." -William Blum
computers excel at math
;-P
humans excel at reason (18/ 83 cent coins?!)
and never the twain shall meet
intellectual property law is philosophically incoherent. it is your moral duty to ignore it or sabotage it
Typical egghead study: look at one thing and propose a change (ha ha) on that basis.
How about the markedly lower time efficiency in the transaction by making the user and clerk do harder addition and subtraction? How about the sheer irritation of doing math like that all day? People generally find it more difficult to perform 29+18+5 than 25+10+5.
Hmm. How difficult? Let's put the pennies aside for a second. The [5, 10, 25, 50, 100] coinage is based upon a cycle of 5, which produces 5 and 0 alternating in the last digit of your accumulating answer. The proposed "efficient" coinage of [5, 18, 25] probably have a cycle of 1. Just by running a test on counting three possible coins (again, ignoring the penny which always has a cycle of 1), we produce at least 6 possible digits (0, 1, 4, 5, 6, 8) in the last digit of the accumulation.
Frankly, I can't see people standing for counting change with this kind of addition going on. We've enough errors and frustration with our coin system based on 1s and 5s.
[You have a stable society when some nut guns down a schoolyard and the law doesn't change.]
A counterfieter decided that he could make a killing with an $18 bill, taking way out in the backwoods of the south. He figured that they were so backwards and out of touch that he could pass it off as a new denomination, like the $2 bill.
So he drives out on dirt roads for hours until he comes to an old country store. He walks in and lays the $18 bill on the counter and asks for change.
"Sure!" says the cashier, "How do you want it: two nines or three sixes?"
Funniest... article... ever.
The reason 25 10 5 and 1 works is because the greedy algorithm for giving change is the algorithm that gives back the least number of coins.
What I am saying is that giving the largest amount back of the highest coin produces the least number of coins. For a given amount, give the highest denomination, subtract that from the total to return, and repeat.
If you work with coins in 25 , 12 , 10, 5, and 1 cent quantities, then the greedy algorithm for giving change fails. for example, the greedy algorithm for 21 cents gives a 12 cent peice, a 5 cent, and 4 pennies for 6 total coins. The least number of coins returned should be 3, two dimes and a penny.
Dynamic programming is used for the proper way to give change efficiently in these cases, but I doubt that people can do that in their head. I certainly can't, and I know what dynamic programming is!
Having 99 coins from 1 to 99 cents would be way more efficient. Exactly 1 coin would be needed for every transaction. And this makes the math a lot easier too.
Nobody cares about pennies any more. Pennies made sense when you could buy a loaf of bread for a dime. Now they just waste everyone's time.
Nickels aren't really worth bothering with, either, but quarters are very popular and convenient, and we wouldn't want to be unable to make exact change for a quarter with lesser coins. I think quarters are a little too big to be the smallest coin, too.
I think the most elegant solution would be to switch to a binary fraction 2-coin system: skip halves, use quarters and eighths. An eighth of a dollar is close to the minimum amount a person cares about, while it has been historically demonstrated that a half-dollar is not significantly preferred to two quarters. I don't think this could happen, though, because everyone's hooked on decimal. Too bad people use their thumbs when they count on their hands.
I was at a fast food establisment yesterday and the bill came to $6.55. I handed the guy a $10 bill, and he gave me back $6.55. When I told him that he had given me the wrong amount back he took the money counted it again, fiddled in the cash drawer, and then handed me back $6.55. At this point i just said thank you, got my food and left only paying $3.45 for a $6.55 meal!
Uhhh...did anyone else have to use a calculator or pencil for this one and go, "Oh, I get it. Those idiot cashiers."?
...snicker...
Any sufficiently well-organized Government is indistinguishable from bullshit.
this is a frickin computer scientist telling people what they should do. Should you have expected something sane and easy for the masses?
:)
Next they'll ask a particle theorist, who'll tell us that the coins should be non-integer multiples of pi, and that the general public should be able to normalize those to 1 since it's an arbitrary unit system anyway.
Old British monetary system
pence written called usage and notes
0.25 1/4d farthing before Edward I, this was usually a penny cut into four pieces; farthing coin discontinued in 1956
0.5 1/2d half penny, ha'penny until Edward I this was usually a penny cut in half; ha'penny coin discontinued in 1971
1 1d penny penny coin discontinued in 1971
2 2d two pence, tuppence 2d coin was made briefly in the 18th century
3 3d three pence, threpney bit 3d coin was silver until 1944, then brass; discontinued in 1971
3.75 33/4d thruppence three farthing
4 4d groats coin made for large part of 19th century
4.5 41/2d fourpence-ha'penny
6 6d sixpence, tanner 6d coin discontinued in 1971
12 1s shilling, bob shilling coin discontinued in 1971
24 2/- or 2s two shillings, two bob, florin florin is 1/10 of a ppound, issued in 1849 to begin transition to decimal money system; florin coin discontinued in 1971
30 2s6d half crown coin discontinued in 1971
48 4s double florin coin made briefly in late 19th century
57 4s9d dollar re-struck Spanish or American dollar, worth 4s9d because of their weight in silver
60 5s crown
65 5s3d quarter guinea coin made up until George III
100 8/4 or 8s4d eight and fourpence
120 10s half sovereign gold coin
130 10s6d half-guinea coin made up until George III
240 £1 pound, sovereign, quid "quid" for "pound" in use 1688-present. "sovereign" for "coin valued at £1" in use 1817-present.
260 21s or £1 1s guinea "guinea" for "coin valued at 21s" in use 1717-1832. Used in auctions (buyer pays 7 guineas, seller gets 7 pounds, auctioneer keeps the difference of 7 shillings)
286 22s6d sovereign (obs.) "sovereign" for "coin valued at 22s" in use 1503-1660
480 £2 two pounds
520 £2 2s double guinea
1200 £5 five pounds
try { do() || do_not(); } catch (JediException err) { yoda(err); }
have already been tried in the us
e gory-leaf.html?alocale=0us
here are some pictures of them from the century before last:
http://list.auctions.shopping.yahoo.com/51521-cat
intellectual property law is philosophically incoherent. it is your moral duty to ignore it or sabotage it
I use my charge card for just about everything, so what does it matter?
In NL, we actually did the 2.5 thing all the way:
5c 10c 25c coins (no 1-cents fortunately)
1 2.5 5 guilder coins
10 25 50 100 250 1000 guilder bills
I wonder what is more efficient, the 1/2/5 or 1/2.5/5 system.
<grub> Reading
Heard on CNN:
"Nick L. Quarter, spokesman for the First National Change Bank, opposes the consideration of an 18-cent coin to replace the dime, as it is un-American. 'My company has a lot invested in dimes, and we feel that 18-cent coins would confuse our customers, staff, and most cashiers. In addition to pennies, nickels, dimes, and quarters, we provide 50-cent coins and the customer's choice of one-dollar coins. There is obviously no need for a new coin.'"
---- Politics: Kissing ass and pointing blames.
I use my credit card for almost everything.
Food, Gas, movies.
Why deal with any change, just use plastic.
No fees, no worrying if you have enough on you.
Interest rate? Pay it off when the statement is due. If you don't have the money, you wouldn't have been able to pay cash anyway.
i really justed wanted to post something with the word quatloos in it. "Five hundred quatloos on the human male!!"
Just Give everyone smart cards and get over it.
If you'd been a really good cashier, you'd be thinking of the "one of each coin" as change for 59 cents.
After reading the summary that is the first thing that came to mind. A great book!
Most people do NOT want to learn how to multiply in sets of 18. We can barely get some people to multiply in sets of 10 cents.
excitingthingstodo.blogspot.com
I just tried to picture a penny...is it round or would my head explode if I could actually picture it?
Any sufficiently well-organized Government is indistinguishable from bullshit.
He also found that change could be done more efficiently in Canada with the introduction of an 83-cent coin and in Europe with the addition of a 1.33- or 1.37-Euro coin. So there is a reason the keep the pound... at 1.37 Euros
Just force vendors to include state tax into the pricing and demonetize the 1 cent coin.
Remember the quarters numbers:
The dimes are stupid obvious.
For nickels, I've come to associate numbers separated by five:
0/5 1/6 2/7 3/8 4/9
And you obviously count ones on pennies.
Half dollars are simple: Use the quarter system.
Start at the quarters, work down. Just keep adding coins at the current level until you exceed the amount you're shooting for. So $1.47:
Pull a $1.00 (who uses the coins for this?)
Quarters: 1=.25 2=.50 : 1 quarter
Dimes: 1=.35 2=.45 : 2 dimes
Nickels: 1=.50 : 0 nickels
Pennies: ".46,.47" : 2 pennies
Now, the .18.
.18 : 1=.43 : 1 eighteen cent piece .18 comes out, it will either not get used, (think of all the machinery not built for four coins - pennies usually aren't accepted now) or it will slow things down.
Pull a $1.00.
Quarters: 1=.25 2=.50 : 1 quarter
Dimes: 1=.53 : 0 Dimes
Nickels: 1=.48 : 0 Nickels
Pennies: ".44,.45,.46,.47"
The extra thought required will slow the change process. It's not that the cashier can't do it, it's that it takes more time to do. If the
Another thing to consider: Most register tills have five coin trays. The unused tray generally holds a couple of rolls of coins. Think about the holdups involved in keeping less extra change in the register.
I've always wondered why we don't just get rid of coins altogether? They are just a pain in the ass. They are heavier than bills and more likely to be lost.
The only advantage I see is for things like vending machines since bill readers suck. But I imagine that could be fixed.
First of all, we can count. No store clerk will wonder anything if you give some coins on top of that 5 or 10 bill to minimize the amount of coins you get back. They do moan a bit over old ladies who like to take this minimization into an artform and spend many minutes digging thru their purse while doing so, but this is mainly due to the other people on the checkout queue starting to roll their eyes after the first minute or so...
:)
And, when changing from our old national currency to euros, we rejected 1urocent and 2urocent coins. While there are 1 and 2 cent coins in europe, they are not used in Finland. Most finnish versions* of those coins are from 'collectors sets' that included one of each type of eurocoin. If you have 1 or 2 cent coins from some other euro system country, they are valid money and are accepted, but all cash transactions are rounded to closest 5 cents - even if you did have exact change to the cent on hand, machines automatically do the rounding. Payments using debit/credit cards and bank account transfers are charged to the exact cent. You can _theoretically_ save a teeny bit of money by 'exploiting' this and paying by cash when the rounding is going in your favour, and using a card when it's not. Of course we are talking about a gain of 1 or 2 cents/purchase, so you have to be really anal over it
There was some whining from people with no math skills how they would 'lose money' due to automatic rounding to closest 5 eurocents (which was outright stupid since during the use of markka, everything was rounded to closest 10 pennies for ages, and to closest 5 pennies before that). It seemed hard for some loud but clueless idiots to understand that over long term the rounding would even out. Sure, if you continously buy single items priced at *.99, you could lose a cent every time its rounded to *.00, but when doing, say, grocery shopping, it's rather random how the final total ends up, so in the long run it's meaningless. And as I stated, if you REALLY care, you can just choose to use a debit or credit card instead of cash.
*) Each euro-zone country manufacturers their own coins. Their 'front' side is identical everywhere, but 'back' side is different in every country. All different versions are valid currency everywhere in the eurozone, and it's kinda cool to notice when ya receive, say, a greek version of some coin in change. Early on the coin pool hasn't mixed that much, but over time you can find ton of different-looking coins from your purse from all over the europe. Those 1 and 2 cent finnish versions are quite rare as they are not in general circulation.
This is ridiculous. The prevailing reason why coins are distributed this way is that you can form denominations of each as combinations of the second. His algorithm requires dynamic programming to reduce coin usage over bizarre combinations and try to teach that to a five year old learning to count money or even your average 30 year old.
The problem is that the paper assumes that prices remain unchanged. Currently prices make strategic use of the nickel and the penny, generating prices that end in .99 and .95. Changing the coinage would likely lead to different price-setting practices -- possibly leading away from the "optimum".
People that come up with dumb ideas like 18 and 29 cent coins should be shot in the back of the head and feed to a pig farm. Along with people who sue because Oreo's have too much fat in them.
Would your theory make the 1 cent coin a mobius strip?
(Heck I'd like to see them make THAT for only a penny!)
What would be interesting would be some analysis of the distribution of the "less than one dollar" part of your change.
By this I mean the part of your change that is given in coins assuming that the whole dollars are returned as bills.
The news item said:
Shallit assumed that every amount of change between 0 and 99 cents is equally likely.
But in reality this is not the case. With prices like $1.99 so common you are much more likely to get a cent back than 99 cents.
Incidentally, there is no need to consider 0 cents change since it doesn't matter what coins are available!
I was recently in the states and as a European found the 25 cent coin rather confusing. Because I'm used to European denominations 1,2,5,10,20,50 I found it really hard to do the sums. For example 37=25+10+1+1 rather than 37=20+10+2 feels odd to me and I have to think very hard to do it. It's amazing how such seemingly small things throw you.
What's the strangest set of coin denominations in use today?
If he had done his math, he would have found that the most balenced form for change is base e, but of course you would need to round it up to 3. With one of every base three coinage, you could always make change for any transaction.
Bel, the mostly sane.. "Of course I can't see anything! I'm standing on the shoulders of idiots." -- Me
Comment removed based on user account deletion
Sure, the amount of coins you receive back will be less on average, but I guarantee that you will spend at least twice as long at the register. Given what I perceive to be the general public's math skills, figuring out how many 18 cent coins to give wouldn't be worth having 17% less coins in my pocket. Time is money, or something. Like has been mentioned in othe rposts, people have enough trouble with quarters and adding / subtracting 25s, let alone 18s.
Sorry, this is just impractical. There's more than one variable in the equation that this guy's not looking at.
Working out all the permutations from 0 to 99 cents, I find that a 1,5,10,25 system returns an average of 4.7 coins, like he says, but I find that his proposed 1,5,18,29 returns 4.45, not the 3.89 that he claims.
Just brute forcing it for me shows the optimum combination to be 1,3,11,37, with 4.1 coins per transaction. I wonder why the numbers are disparate. Anyone else running through it?
Granted that this researcher knows that his theory will save time in the future, but I see this as complicating the problem even more. Even I have a hard time working with numbers. Your average human being living in any nation that has a currency system will not be able to comprehend using "odd change" when giving change to another person. Our brains have been trained to think of coins as "units of a whole" (dollar, pound sterling, etc...) The reason why you see 1-cent, 5-cent, 10-cent, 25-cent, and half-dollars in the US is because a certain number of any one of these coins will be equal to one dollar. And when someone gives change, it's much easier to give 23 cents as a dime and 3 pennies instead of 1 18-cent piece and a nickel.
At
http://www.euroswapper.com
you can find the images of all (8 * 15 = 120) different euro coins!
jsinnema
What, people still use coins? Isn't that why god created credit cards?
Actually, I was in Guatemala a couple months ago haggling over the price of a hammok in a small shop. After the haggling was over, I noticed a visa sticker on the wall. I handed over my card and paid for my negociated price with a credit card. The whole experience was a bit surreal. It really is nearly everywhere I want to be.
I think instead of worrying about improving our current change system, we should go ahead and work on heading twards a completely cashless society. If small shops in Guatemala can accept my credic card, why won't the damn movie theatre?
Mod my comments down. It'll be fun.
it's plain wrong!
-
doesn't this guy have anything better to do with his joules?
An 83 cent coin might make change distribution more efficient, given today's model of pricing. However, once you change the coinage, some types of pricing may change as well, simply to accomodate customers. Something that is $1.99 now may become $1.83 or $1.66 (or probably $2.49). Since pricing patterns will change, the ideal amount of coins to dispense may or may not change to accomodate it. Then you have to rework your original plan. Plus, it would blow the hell out of Walmart's pricing. ;-)
I beleive this is the answer. But I don't remember the title of the book.
I thought the Altarian Dollar monetairy system had a 42 cents coin...
Wenn ist das Nunstueck git und Slotermeyer? Ja! Beiherhund das Oder die Flipperwaldt gersput.
One of the nice things about the current set of denominations is that you can make change most efficiently (fewest coins) by starting with the highest denominations and moving down to pennies. For example, to make change of 36 cents, you start with 1 quarter, then 1 dime, then 1 penny. Three coins total.
However, with this newly proposed solution, this is not always the case. Using the above algorithm with the 1-5-18-25 denominations would yeild, 1 quarter, 2 nickels, 1 penny. However, the most efficient change is actually two 18-cent pieces.
So while it may yeild more efficient solutions, is it more difficult to compute that more efficient solution. Therefore, it may in fact lead to less efficient use.
...it's not even April 1.
Why don't they round everything to the nearest 10c and do away with 1,2,5.
We had 1, 2, 3, 5, 10, 15, 20 and 50 denomation coins.
As well as 1, 3, 5, 10, 25, 50 and 100 bills.
If I remember correctly, "3" bill was most-widely used. Makes me wonder why US doesn't really use $2 bills.
The Deivation assumes two falacies
first,
that the price of goods is not partly determined by the demoninations of coins. for example, the reason why a candy bar is 50 cents or 65 cents and not say 48 cents is because we have nickels dimes and quarters. or that the reason a price is 5.95 cents and not 5.96 cents. etc..
Second,
this assumes your change purse is stocked with all denominations. that's true at the cash register but not in my pocket. When I reach in my pocket and I pull out some change there are a myraid of ways I can make 25 cents. 5 nickels, 2 dimes and a nickel, 5 pennies+ etc...,
not so with his optimal set. if I'm nissing any of the denominations its hard to make it up with the others.
third, entropy
again reaching for change in my pocket the goal is not to find the minumum number of coins but rather to be able to pay the bill without thinking too much. that is the more ways I can add up to the same value the more likely I will on a random grab find the right coins to make it. I dont care how many coins.
Some drink at the fountain of knowledge. Others just gargle.
Sorry, but that's an invalid assumption. I see even $ amounts in my transactions far less than the expected 1% for example. For example, go buy one of anything at $x.99, then add tax. It's very unlikely that you will end up at $y.00 for the bill. Which are there more sales of in a given day: sales of large numbers of items in which random might not be a bad guess OR $N of gas + a candy bar which will be priced far from random?
This is the same problem as sorting data that is not uniformly distributed. Knowing the frequency distribution can speed your algorithm. Knowing the pricing schema should bias your coinage selection. That immediately introduces problems, however. Consider different sales tax rates in the many jurisdictions of the US -- that implies different biases and regionally optimal coinage choices. The really interesting question is: are there coinage choices that are optimal for one tax rate (say 5%) and horrible for another (6%)? This is similar to the way qsort is generally somewhere on O(nlog(n)) but for data in perfect reverse order it runs to O(n^2). It's interesting that this guy has worked out a model, but in order to be interesting it needs to be convolved with real world pricing.
Well, I redid the calculation and found that the optimal coin denomination would be 18.333 cents
Get a life you crazy faggot! That's not funny, okay?!
People like what is familiar and avoid change as much as possible. I'm old enough to remember the failed attempts to convert us Americans to the metric system.
Also, this works very neatly in mathematics, but nowhere near as neat in reality. An 18-cent coin is so uneven in our decimal mindset. Imagine having to add up the change in your pocket. Pull out a quarter, two 18-cent coins, three nickels, and eight pennies -- er, um 25+18? does anyone have paper handy - okay 43. now add 18 again ........ oh, hell.
The big thing that has been forgotten with these optimized coins is that we like to have our coinage in denominations that can add up to an even dollar. 18x5=90 and 18x6=108. 29*3=72 and 29*4=116. Converting spare change to bills would be a major hassle.
I was taking one day at a time, but then several days got together and ambushed me. (from a Rhymes with Orange comic)
He ignores the constraint that coins must total up to a whole number of dollars - otherwise breaking a dollar would be unfeasible.
This applies for arcades, tolls, etc.
If this is an application of the scientific method, then what is a high school math story problem?
Marcy: "... that's as dumb as your idea for the 99 cent coin."
Steve: "That wasn't dumb!!"
Marcy: "What about tax?"
Steve: *sigh* "You sould just like the poeple at the mint."
seems to me that multiples of the whole number which is closest to e would be more efficient, if you -really- want to minimize the number of coin&bills used in each transaction.
:)
coin of 1, 3, 9, 27, 81 cents,
bills in 243, 729, 2187, 6561 cents.
good luck getting people to memorize those multiples. (don't they have cash registers which tell the cashier how much of which coins to return as change?) getting change twice (or more) for the same transaction could confuse people too.
anywho, this sort of silliness is what happens when efficiency is taken too far, or in the wrong direction. (remember: efficiency is building the train tracks right up to the gas chamber.)
note also that 3 is the optimum number of choices in each menu of a large telephone menu tree.
Of course, it would be awhile before we could get cash registers that could round up to the nearest 5 cents or so, but it would lighten the load in my pockets (giving me more room for gadgets).
Just remember, there used to be a half-penny in many countries, but it was eliminated due to almost-complete lack of worth. Now it's time for the penny to follow that same path.
Of course, in Canada, we get to deal with coins for our $1 and $2 denominations.
"Reality is merely an illusion, albeit a very persistent one " -Albert Einstein
These suggestions might be very well right now, but what about in the future? Coins last for a long time. I'm pretty sure that inflation change the equation a bit.
In a few years we'll all be swiping plastic or leaving a thumbprint/retinal scan and the funds debited out of our account automatically.
Back in the long ago, people used to do this. Spanish coins could be broken into eight pieces: "Pieces of Eight". The whole coin was the equivalent of a dollar, so a quarter would literally be a quarter of the coin, or two bits.
"I'm not impatient. I just hate waiting." - My Dad
Hard currency is vital for privacy when making purchases. This might sound stupid, but if someone was daft enough to field odd coinage, I guarantee that the number of people using credit cards would increase noticably, even for small transactions.
And no wisecracks about what I spend hard currency on please...
Okay, here's my idea for U.S. change reform (no, that's not redundant).
How about we just get rid of the damn penny? I know, I know, "A penny saved is a penny earned." Guess what - Ben Franklin said that two hundred friggin years ago. Adjusted for inflation we should be walking around saying, "ya know, 5 bucks saved is 5 bucks earned."
If Franklin were alive today, he'd think we were retards for scrounging around for such piddly sums of money.
I'm not saying we need to eradicate all pennies, but how about we just stop minting them? Anyone?
Unfortunately, the sales tax rate is not the same everywhere. When I buy a coffee at the Starbucks in Sherman, TX, where I live, it costs $1.51. However, when I drive into Dallas for work and buy the same kind of Starbucks coffee, it costs $1.52. This is because I'm paying an extra DART (Dallas Area Rapid Transit) tax that I don't pay in Sherman.
If stores were to include the tax into a nice round number, then they will essentially have to charge less for the same product in Dallas than they would in outlying areas.
For the longest time, I have advocated just whacking the last decimal place off and getting rid of pennies, nickles, and quarters altogether. Circulate a half dollar with a face on it that nobody will collect (like Tammy Fae Baker). Let's face it, the penny is an outmoded unit.
Mythological Beast
Wake up - the future is arriving faster than you think.
A few years back, my dad was paying for something, and paid an uneven amount in order to get even change. The clerk looked at the money, sort of shrugged, and punched it in and started counting out the change. The catch is---my dad misheard the amount. So when the clerk started counting out a bunch of pennies and nickels, my dad was like, "wait, what?" Had the clerk had *any idea* why my dad had given an uneven amount, she would have realised that he'd misheard the price. But she just punched it in and started counting it out....
A few years after that, my sister (in 5th grade at the time) had a test with a miscalculated grade, and when my mom went in for a parent-teacher conference, she brought it up. In particular, she said she'd added up the number correct and divided by the total number of questions, and got a different percentage... the teacher looked down her nose at my mom and said, "that's *not* how it's calculated." How was it calculated? Well, you have these cardboard discs that you turn according to the total number of questions, and then you read the grade out of the little window corresponding to the number right.... This woman had only the vaguest notion that this grade was a percentage correct, and *no idea at all* that---as a percentage---it could also be calculated by dividing the numbers out. None.
``This, too, shall pass.'' ---Eastern proverb
USD is dying
Yet another crippling bombshell hit the beleaguered USD community when last month XE confirmed that USD is worth less than ?0,86 and £0.61! . Coming on the heels of the latest XE survey which plainly states that USD has lost more market value, this news serves to reinforce what we've known all along. USD is collapsing in complete disarray, as further exemplified by failing dead last in the recent survey of currencies.
You don't need to be a pointy haired analystto predict USD's future. The hand writing is on the wall: USD faces a bleak future. In fact there won't be any future at all for USD because *USD is dying. Things are looking very bad for USD. As many of us are already aware, USD continues to lose market value. Red ink flows like a river of blood. The one dollar note is the most endangered of them all.
Let's keep to the facts and look at the numbers.
OpenBSD leader Theo states that there are 7000 users of USD. How many users of INR are there? Let's see. The number of INR versus USD posts on Usenet is roughly in ratio of 5 to 1. Therefore there are about 7000/5 = 1400 INR users. IRR posts on Usenet are about half of the volume of INR posts. Therefore there are about 700 users of IRR. A recent article put Euro (?) at about 80 percent of the currency market. Therefore there are (7000+1400+700)*4 = 36400 Euro users. This is consistent with the number of Euro Usenet posts.
Due to the troubles of USA, Terrorist threats and so on, USD went out of business and was taken over by INR who sell another troubled currency. Now INR is also dead, its corpse turned over to yet another charnel house.
All major surveys show that USD has steadily declined in market share. USD is very sick and its long term survival prospects are very dim. If *BSD is to survive at all it will be among OS hobbyist dabblers. USD continues to decay. Nothing short of a miracle could save it at this point in time. For all practical purposes, USD is dead.
Fact : USD = ?0,86 and falling!
Cecil has the right answer instead of this complete conjecture.
Hey, I can beat this guy at this math thing. According to my calculations there are much more efficient combinations. For example, if you use the coins 1, 2, 4, 8, 16, 32, 64 it will take approximately 3.19 coins per transaction (this is simple binary arithmetic). That's way better than his system which takes 3.89 coins per transaction. The only problem is that the geeks will do just fine with these denominations but just try and ask the average waitress to make change using those coins. Go ahead and ask, I'm sure it will work out just fine! :)
You know, if we mint 1 coin for every amount of change (like a 57 cent coin, a 58 cent one, etc.) then it will only take 1 coin per transaction. Of course then we have to worry about having 99 different coins, making them distinguishable from each other, etc.
The current United States system of currency works just fine. Denominations of 1, 5, 10, 25 are easy enough to calculate and efficient enough for all intensive purposes. Sure this proposed new system may be 17% "more efficient" for a computer but real people need to use the system also.
Some things are best off just left alone...
Sapere aude!
I'd say the efficiency he speaks of would only work if everyone making the transaction was a computer.
But hey, isn't that the case if you use a bank card or credit card for transactions instead of cash?
It's just decimal places, not metal circles that way.
I was about to say I mostly use plastic for transactions, but I know it can't be true because I just took a gallon jug full of change (accumulated over three years) to be changed in ($335.17) the other day, so I must use currency for something.
Chris
If the minimum-wage casheers were all computer scientists.. It's challenging enough to figure change on a 5-based system (5,10,25); Try introducing odd-count change... Quickly, how much change (25,10,5) does it take to make $0.80.. Now do the same excersize with 18 and 29 cent pieces!
-- Greg
Slashdot, would a spell-checker for posting be too much to ask? It's not rocket science!
Well Bin laden and Saddam met in the cave and figured out that having millions of USD at a 1% interest is stupid when you can have Can dollars at 3% interest that goes up in value when more people buy it ...
...
...
...
...
And the Canadian dollars is low because most of the Canadien government money is in USD because whe whant those 286 million people buying our product to make work for our 32 millions
The next big revolution is going to be when US citizen figure out that in our Canadian Bank there money is protected up to 60 000$ , our bank never go bankrupt and our money is easier to buy then the USD and its actually going up
and Enron style company only work in the US
Our big fund are not managed by the same people and are very well divided
I think if we just got rid of pennies (since they're not worth crap) and rounded everything to the nearest 5 cents, it would be the most efficient.
Something which is obviously untrue. Amounts of change tend to fall in the low or high range, not the middle.
This is just silly. One of the reasons we have the denominations we do is b/c it makes math easy. Could you imagine the high school drop out behind the 7-11 counter trying to figure out how many 18 cent pieces they had to give out.
And the coin to make transactions with canada and the EU is silly as well. The exchanges rates fluctuate....should we coin a new coin each time they change?
Another out of work mathematician with nothing better to do. Kind of like the twits that invented statistics. Who cares.
Professional Politicians are not the solution, they ARE the problem.
Is this a valid assumption? Most of my change comes from small purchases, and the vast majority of small cost items have similar prices (i.e. 0.99, 1.29, 1.50, 4.95, etc). The amount of change from each of many small purchases will tend to fall into a few discreet values, and would not follow a uniform random distribution.
It's just sometimes people like to do this to be helpful or just to be annoying/arrogant (really anticipating the look of panic in the cashiers eyes).
Meanwhile, I'm behind these dumbasses in line waiting to pay for a goddamn quart of milk.
If anyone ever made me make change lke that I'd treat them the same as if they were trying to rob my store, pull out a baseball bat, and hop over the counter chasing their silly ass out of the store.
cracks bat against ribs..
"next time you'll give me bills and quarters, WON'T YOU?..."
another wack in the ribs..
"WON'T YOU."
Him: "pleaaaase stoooop.."
"Die fucker!!"
whack, whack whack!
why run from Vincenzo?
1. Any combination of coins should represent a reasonable amount of currency.
2. A change system must be able to represent any reasonable non-negative amount of currency.
For all the definitions of reasonable that I'm likely to use, the first condition is equivalent to "all coins values are a positive integer number of cents" (i.e. no hay-pennies, and no coins that have negative value); the second is equivalent to requiring a penny.
3. It should be possible to figure out the best way to make change (meaning, fewest coins used) in a "good" system by following this naive greedy algorithm: first give out as many of the largest denomination as possible without exceeding the total you want to give out, then as many of the next largest, etc.
In C-like pseudocode, this algorithm would be:4. (a refinement) In a "really good" change system it should be possible to use an even more naive algorithm; this algorithm is best demonstrated in pseudocode:Note that our current system satisfies criterion 3, but not criterion 4. Our current system without the quarter (but with the half dollar) satisfies criterion 4. An example of a system that does not satisfy criterion 3 is [1,5,10,18]. (In that system, the naive greedy algorithm would make 20 as 18+1+1, whereas 10+10 uses fewer coins)
It's easy to show that satisfying criterion 4 implies satisfying criterion 3. It's also pretty easy to show that a sufficient condition for criterion 4 isfor all i so that the indices make sense.
However, what I've never really sat down to work on (*) is whether this condition is really necessary for criterion 4, and what necessary and sufficient conditions are for criterion 3.
Efficiency in terms of numbers of coins used never even occurred to me, though I'm sure it would have if I lived in a country with a purely decimal coinage system (i.e. just penny, dime, and dollar coins)
(*) Or if I have, I've forgotten. I tend to do that when I don't write stuff down.
In the UK we have 1, 2, 5, 10, 20 and 50 pence coins, by my reckoning this gives an average of 3.4343 coins to make from change from 1-99 pence.
;o)
Come on guys catch up
In order to get a more realistic/useful result, one could get a good-sized random sample of actual change amounts given if one had access to a few days of cash register data from some large retailers, and then run the analysis on that.
Assuming a uniform (or some other nice, clean distribution) may make the problem easier, but it doesn't necessarily lead to a conclusion that has anything to do with reality (i.e., GIGO).
How did the idea of the economically rational individual ever persist, in the face of things that cost $9.99?
The greedy algorithm (as many as possible of the largest coin, then work down) is also the minimal (fewest number of coins) algorithm for some sets of coins. However, as has been pointed out, 1, 40, 41 is not one of those sets.
The old (pre 1971) British currency was of this type:
1, 3, 6, 12, 24, 30, 60
Consider making change for 48.
My question: is there a simple way of determining whether the greedy algorithm is optimal based on the coin set?
with denominations that do not divide evenly into each other it is non-trivial to find the optimal change for a given transaction.
..., c_k$, such that $\Sigma_{i=0}^k = n$ where $n$ is the amount of money in cents to change. Assume that we remove the coin with the largest value. The remaining coins, $c_2, ..., c_k$, represent the solution to the sub problem of changing $(n - c_1)$. If $c_2, ..., c_k$ is not optimal there exists another set of coins for this subproblem, $x_2, ..., x_k$, such that this solution has fewer coins. However this is a contradiction because we can now form a solution for the original problem, $n$, by combining $c_1$ with $x_2, ..., x_k$ that has a smaller size than the original optimal problem. This is a contradiction and hence $c_2, ..., c_k$ is an optimal answer to the subproblem and therefore the coin changing problem exhibits optimal substructure.
..., C(n-d_k)\}$.
whereas with the US denomination (and most denominations are designed for this reason) you can use a greedy algorithm to give back change (always choose the largest coin possible, repeat) and you are guaranteed to be giving back the fewest coins.
you can prove that a greedy algorithm provides an optimal solution if the problem has optimal substructure and the greedy choice property.
To prove optimal substructure consider a collection of coins for an optimal solution, $c_1,
To prove the greedy choice property we must show that a globally optimal solution can be arrived at by making a locally optimal, this is, greedy, choice.
For this particular set of American denominations we can prove the greedy property with a proof by contradiction. If the greedy choice were not optimal there would be an optimal collection such that:
1. some set of dimes, nickels, pennies added to more than 25 cents or
2. some set of nickels, pennies added to more than 10 cents or
3. some set of pennies added to more than 5 cents
However, all of these situations are impossible. If some set of pennies add to more than 5 cents, simply replace 5 pennies with a nickel (the greedy algorithm is better). If some set of nickel and pennies add to more than 10 cents and if there are two nickels, replace them with a dime; If there are a nickel and the rest pennies,
replace a nickel and 5 pennies with a dime. The same holds for a quarter. If three dimes, replace it with a quarter and a nickel. If it's two dimes and nickel/pennies, replace it with a quarter. And so on... The property of the coins that results in the greedy property is that each coin denomination divides evenly into the next larger coin denomination. Therefore each larger coin denomination that is removed must be replaced by at least two additional coins.
With non-even denominations you are required to actually search an n^2 space for the correct set of denominations. in fact, the algorithm is:
$C(n) = 1 + min \{C(n-d_1), C(n-d_2),
Additionally, $C(n) = 0$ for $n = 0$. We can ignore $n 0$ are we just define $C(n 0) = \infty$. By building the array in time/size $\Theta(nk)$, and keeping track at each step which value of was chosen for the minimum, then we can list the coins by tracing backwards through these recorded values. This augmentation takes no additional time since it can be done during building the array in time $\Theta(1)$.
So, basically you've changed the problem from a linear time algorithm in the amount of change to a quadratic time algorithm in the amount of change...
GOOD LUCK WALMART EMPLOYEES!
I don't know about anyone else, but I'm seeing more and more Sacagewea dollars recently, which gives us a 5 coin system in the US. The article also refers to the unpopular Kennedy half-dollar coin, which gives us a 6 coin system.
An 18 cent coin just seems silly to me, because the calculations required to use it would be difficult to easily optimise in your head. In the UK, we have a 2p coin [ironically, one of the largest-diametered in circulation] and wouldn't this cut down the number of coins needed in an easily calculable way ? It seems to me, that ease of change calculation is as equally important as the average number of coins used for said change, but this is almost glossed over in the article by one sentence.
Why not coins in 1, 2, 4, 8 etc units?
Sure, there would be more coins needed but the advantages are the simplicity, quickness (at least for those who understand binary) and a very high probability that one is able to change even when there are not too many coins left. And all the computer freaks would love it!
Unix makes easy tasks hard and hard tasks possible. Windows makes easy tasks easy and hard tasks $29.95.
"Can you give me change for an $18 bill?", he asked the gizzled proprieter.
"Shore! What'll it be? Two nines, or three sixes?"
because nobody is going to use coin denominations that they cannot add up simply in their head.
Insightful points to be sure.
The computer tells the cashier to give back 98 cents, not "6 times the coin 18, ..." etc.
So your argument is moot: The cashier does actually have to use math to give you back your change.
I heard that the original practice began in the early 20th century. Some newspaper owner was breaking into the business, and his gimmick would be "penny newspapers." In order to enourage people to buy it, he pressured local businesses to drop their prices by one cent. He was successful and the practice caught on.
Pennies are worthless?!?!?
Meet my penny-filled sock, my friend! And the sock is stinky, too!
(Gimme a break, it's noon on Friday and I'm bored outta my mind...)-
Vote monkeys into Congress. They are cheaper and more trustworthy.
1, 01, 001!
Sure, you get more change, but imagine a beowulf cluster of these!
"Don't you know you're going to shock the monkey?"- Peter Gabriel
"What's the strangest set of coin denominations in use today?" That would be the used condom collection used by the Royal Scots Guard. Being too thrifty to dispose of the condoms, they recycle then and use them as means of exchange.
I'm not sure that I understand the article. When I want to buy something, I hand over my credit card, and I don't get any shiny round things handed back to me.
:-)
Oh, you mean using cash to pay? How utterly 20th century...
We already have a $1 coin that has a distinctive feel in your pocket (one of the reasons why the Susan B. Anthony dollar sucked). The problem is that people just won't use them.
I lived in Germany from 1993-1997 and I loved how practical the 1+ DM coins where. Each was distinctive so you could count the change just by shuffling the coins in your pocket, and they last a hell of a lot longer than bank notes. The money I got to see in France and Luxemburg had the same practical touches (the Lux money was so cool I carried a few notes in my wallet for probably 3 years after I came back to the states).
We need a real 50 cent coin, more use of the $1 coin and hopefully a $2 piece too. Or screw the coins and let's come up with a real smart card for small purchases. The smart card used in the DC Metro system is practical as hell, and the Mobil SpeedPass is really nice too.
Pedro
----
The Insomniac Coder
But stupid prices like 19.99 and 19.95. I hope every store that uses that price format would just go out of business. Use whole or half units. That should be accurate enough!
J.
Just look at yourselves. How much money do you spend to print out all the currency? How much money do you spend on computers to count it for you? How much money do you spend on scientific studies of how that currency is used? How much time do you and everyone you know and all the store checkers spend counting out those coins and bills? Time is money. How much time do you spend doing your taxes? How many people are employeed by the IRS? National Treasury? Banks? Credit institutions?
All forms of entertainment, all forms of news and public information and politics exist for one purpose. Money. They don't play ball because they like it, they play to get paid. We let them play so we can get paid. We work to get paid. And we run for office to get paid.
When will all of this finally sink in that all of the inefficiency and corruption in the system is caused by MONEY!
Just get rid of it, let the computers manage our resources and work together to create a communist socialist democracy, a government of the people by the people for the people who's purpose is to see to it that every person in their nation is provided for. That means that they are given the proper environment for education and the pursuit of happiness among other things. We need cooperation and community here, not individuality and selfishness.
Or else we might as well just work the rest of our lives to pay for all the commercials and war, to pay for all the money.
<voice style="school house rock">
18...36...54...72...90....108
STOP
Multiply by 18 is like multiplying by 20 but subtracting multiples of 2. So 18*3 is really like 20*3 - 2*3. That's just 60 - 6, or 54! Let's do it again!
18...36...54...72...90...108...126...144...162.. .180!
Ready or not, here I come!
</voice>
no, I didn't use a calculator. I sure hope the math is right.
electronic cash cards
;-P
no change at all
seriously, why haven't these taken over the world yet?
and where's my damn rocket car! i was promised a rocket car you know!
intellectual property law is philosophically incoherent. it is your moral duty to ignore it or sabotage it
About the difficulties involved in making change with a small stock of coins.
That's definitely a refinement that needs to be made to this model, even if we make the (blatantly false, but false in a way that leads to interesting research) assumption that human brains do integer operations with the same speed tradeoffs as binary computers.
I'm not quite certain how you'd model this, and how you'd measure the "small coin stock robustness" of a coin denomination system, but it's definitely at least as interesting a problem as the original.
Whatever happened to the idea about using a balanced ternary system of money?
---If you can't trust a nerd, who can you trust?
Just get rid of all those other coins and just use pennies!
"They say travel broadens the mind, so I went over the falls in a barrel." -Thomas Dolby
Well, duh....
1, 10, 100!
(don't blame me, it's the lack of coffee!)
"Don't you know you're going to shock the monkey?"- Peter Gabriel
Forget $1 coins, I want a $1.0753875 coin so I can buy things that cost 99 cents.
I thought that this was an old mathematical puzzle? I'm sure that I've seen this before... Hmm. Maybe that's why they call it REsearch?
I believe that what the researcher failed to take into account is the way that the human mind works. Adding 1's, 5's, 10's and 25's is definately easier than adding 1.37's or 83's for us.
Sure, it may make the handing out of change more efficient by lowering the average amount of change given from 4.x to 3.x coins, but that efficiency will be more than lost when the clerks at the local mini-mart -- who already have problems giving out the correct change -- have to figure out that my $0.72 in change will be two 29-cent coins, two 5-cent coins and four 1-cent coins.
Not to mention the increasing size of cash drawer shortages caused by less-than-mathematically-inclined clerks.
Is it just me, or does it seem that the less "rounded" education becomes, the more one-dimensional "solutions" appear? Guess it is more true than ever: when all you have is a hammer, everything looks like a nail.
There's so little difference between politics and jihad lately...
This article is a complete waste of time. This might be a fun paper for a discussion about coinage, but it fails horribly when taken as practical advice.
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The US does not need another coin. Indeed, the *opposite* is true. If you get rid of the penny, you can increase efficiency tremendously, to only 2.75 coins per transaction, and a whopping 45% of transactions would require 2 or fewer coins!
Many people oppose the elimination of the penny, but bear with me for a moment. Consider the following issues:
- Pennies cannot be used in vending machines, and therefore are not as "spendable" as all the other coins.
- Prices will not rise as people think they will; they will fall instead! Everything that is priced at $n.99 will now be $n.95 instead (marketers HATE to price in round dollars because it makes their prices look higher). All other numbers will be rounded to the nearest $n.n5.
- The US government makes 12 billion pennies at a cost of $100 million each year (http://www.retirethepenny.org/), which could be put to better use than filling up my coin jar.
- Half of these pennies will disappear from circulation within a year! (http://www.shepherd-express.com/shepherd/19/41/n
- Counting out pennies costs the economy an estimated $20 billion in productivity annually (http://www.retirethepenny.org/)
- The U.S. Mint loses $8 million a year manufacturing pennies. (http://www.shepherd-express.com/shepherd/19/41/n
Think about it - do you *really* want another coin in your pocket? Thank God that politicians don't listen to us all the time!
-Mark
Several years ago, our (ahem) wonderful PM proposed bringing the Value-Added system, whereas all retail prices would already include the GST. This would mean that, on a province-by-province basis, retailers would only have to add the PST, if there was one. Would have made things MUCH easier. Who knows why they didn't go through with it (I'm sure someone here knows... but I don't).
As I understand it, the Brits have been doing it this way for years.
Visit us at http://www.iblist.com!
1.37 Euro coin? Yeah, this guys on crack. I still have a wad of coins I couldn't get rid of from my Europe trip a few months ago. I don't need a more efficient way to get more coins. Just my 2 Euro Cent coin's worth. (I have three) -E
As tax rates change the Optimum Coin value will also change so over time There will be many many coins wich would be a good thing for coin collectors.. But poor for Currency management... Pennies are rarely used from my experience.. Most people are in a rush to sit and count out exact change most times when buying something.. and Pennies usually get thrown into jars and what not and saved up in massive bulk to be taken to the bank ect.... Eliminating pennies would show a promising reduction in the ammount of coins returned..
Who needs WiFi when we can have Packet Over Sheep! http://datacomm.org/PoS-InternetDraft.txt
Firstly, I think at least one person has done this some years ago.
Secondly: "In finding coin denominations that minimize the average cost of making change, Shallit assumed that every amount of change between 0 and 99 cents is equally likely."
I suspect the distribution is different in countries where 19.95 prices are common.
Similarly for countries where 18.88 prices are common (many chinese regard 8 as an auspicious number, while 4 is inauspicious).
Then there are sales, gov taxes, service charges etc.
Also, would the efficiencies bear out over multiple transactions in a complete cycle? e.g. I have a random bunch of coins, I give you change, I have fewer coins, with those few coins left would it still be easier to give change to the next person?
It makes the "change" algorithm harder - the "biggest first" algorithm doesn't work as well.
Given the theoretical improvement is only about one coin on average, I doubt it's really worth it.
Just one of those academic exercises.
at my work cafeteria. The manager of the cafeteria said that by doing this, "I made the cashiers feel stupid."
I tried pointing out that this was grade 3 math and it made it easier for the cashier because they would have to return less change. The advantage to me was there was less shrapnel in my pocket.
The upside was that I could go out whenever I wanted because the cafeteria refused to serve me. (See the previous article about dodge work).
myke
Mimetics Inc. Twitter
* 2.79 coins average per transaction given that getting 5 cents is just as probable as getting 95 cents, and that no 50-cent pieces are used.
* Counting in 5's, 10s, and 25's is a lot easier.
* Saving pennies, rolling them up, going to the bank, and then driving home is a pain-in-the-ass, and honestly isn't worth my time, e.g. 2 hours of work to get $10 of pennies?!?!?. It's more economical to throw the friggen ugly coins in the trash, but I can't do that out of principle.
GET RID OF THE PENNY!
I prefer the following : make pennies worth $1.
This would:
-eliminate the penny,
-give us a distinguishable dollar coin,
-and stimulate the economy
Pennies are visibly and tactilly different from our other coins; can be used in vending machines; are easy to carry around. Plus, Lincoln was a great guy, what with freeing the slaves and all (better than that indian-killer Jackson that's on the $20, at least) and this lets us honor him once again.
Income would be redistributed somewhat randomly to people with big jars of pennies. The ultra-rich (you know, the ones getting the big tax cuts) probably have no more than a handfull of pennies. Some people would chose to hoard the new dollars; while others would spend them with abandon. And wouldn't you like to pay your taxes by sending in several rolls of pennies?
Just for laughs, I'd make "wheat cents" worth $100.
Someone mod the parent up. This is a good summary of the article's purpose, which some people seem to be missing.
This is just mathematics, people. Sometimes Mathematicians do things because something catches their eye.
We've been rounding tax and all to the nearest penny for a long, long time. Rounding to the nearest nickel won't hurt anything.
We also wish to have a minimum currency, which we take to be a penny. Thus an integral number of pennies must equal any other coin.
With these two, perfectly reasonable requirements the current system of penny, nickel, dime, quarter is optimal. The only remaining valid coins are 50 cent pieces (used but rarely), 20 cent pieces, 4 cent pieces, and 2 cent pieces.
His optimization problem was under-constrained. No wonder he didn't get a unique answer.
I just failed to find any of my one sided pennies....Curse you third dimension!
First, can't you tell a joke when you see one? (By joke I don't mean the maths is wrong, just that obviously the writer wasn't intending that we move to 18c coins).
Second, what is easy is what comes with practice. Currencies, like most other measurement systems, were not originally decimal, but duodecimal (i.e. using base 12) and various multiples thereof. Right up to the 1970s, the UK used a currency system which had 12 pennies to a shilling and 20 shillings to a pound. The US and UK still use duodecimal for weights and measures (think pounds and feet) and the whole world uses it for time (12/24 hour systems) and angles (360 degrees is 30 times 12).
Why were systems based on numbers like 6, 12, 24, 360 etc. so common, given that we tend to count in decimal? Well, they have large numbers of factors. In other words, while they might be harder to add and subtract in your head than decimal systems, they're much easier to do division with. And since division is much harder to do in mental arithmetic than addition, that's a big advantage.
For example, with 12 ounces in a pound, I can take a half, a third, a quarter, a sixth or a twelth of a pound and still be dealing in whole ounces. With a decimal system, 10 has only 2 factors: 2 and 5. So to buy a quarter of something devised in a decimal system you end up with 2.5.
Now that also has a knock-on effect when making change. Because of the limited factorisation of 10, most decimal systems divide things into 100s or 1000s.
Result: in a decimal currency, you end up not with 10 cents per dollar, but with 100 cents. And that's the real reason you have so much change in your pocket. If we had 12 cents to the dollar (or euro), then by copying the old british system -- with a 1c, 2c, 3c and 6c coin -- you'd never need more than 4 coins to make change from a shilling.
And would the cashier at WalMart be able to handle it? Well first off, maybe if as a result they had to think more as kids they'd be better off at maths to start with. And secondly, since they have to use a calculator now anyway, what would be the difference?
The author of this post asserts his moral rights.
We have computers and scanner thingies all over. Why aren't we moving toward digital cash? I use my debit card for almost everything already, it wouldn't be that much different to have "cash machines" dispense cards like Metro cards.
This would also have the added benefit of anyone smart enough to hack it having more money...I think that's fair.
Long ago in an undergrad computing theory course, we proved that the most efficient counting system was base-e, with each place in a number being a power of Napier's constant, e.
However, since every power of e is transcendental, every whole number would be an infinite decimal.
Thus proving that efficiency is not always practical.
Base-2 is close enough, but base-3 would be closer.
It doesn't matter what the denomination is. As long as change has to be made, some patrons will receive the wrong change.
Lots of cashiers don't know how to make change. Many have been trained to do it wrong. The most common error is the cashier puts the large bill the customer just handed them into the drawer before giving the customer change and watching them count it. There used to be a little slot between the plastic guard and the metal cash register enclosure that was perfect for temporarily storing that large bill in customer sight. When the customer looks at you after counting his money, pause to see whether he questions it, then put the large bill in the drawer and close it.
Adding this momentary delay before putting the customer's large bill in the drawer and closing it, protects the cashier and the customer from being short changed.
I've seen managers put large bills in the drawer before I counted my change. One gave me change for $10 instead of change for a $20. I'm a creature of habit. When I hand a cashier a large bill, I always say, "outta twenty" or whatever the bill is. I'm sure I did that with this one. But she'd already put the bill in the drawer and insisted upon a recount of the drawer and by the time she did, my food was cold. That is not the way to do things. When I pointed out her mistake, she lost her temper. Then I lost mine.
I was trained on older cash registers to do things this way by a store manager who was very particular about this. He's been in business for more than 30 years and says he's never had a dispute with a customer over incorrect change. Way back then, you had to actually count the coin change. Many of the newer cash registers do this for you. I wonder how many of today's cashiers could make change in their heads.
What's my point? Most point of sale problems concerning change making are due to lack of skill and/or poor training of the cashier. Using more efficient denominations or pricing items to the nearest buck won't fix this.
Wansu, th' chinese sailor
Just do away with money and tattoo an invisible barcode on everyones' head.
No heavy change, no filthy money, no robberies, far less crime, zero fraud, faster checkouts.
Problem solved! Just take the MARK...
In the land of the integer-multiple-fixated, all that stuff to the right of the decimal place is just not good.
The Russians have won. They have made the world a cesspool of distrust, greed, fear and hate.
Or does it have a Mobius strip edge?
Or maybe its a Klien bottle (now if I could make one of these I'd probably not use it for change).
Or ... ?
Of the stores that might worry about this efficiency problem, they could more easily just charge more roundish numbers in most cases, if that were a concern. But it is not of primary concern to them, on the grounds that it is all about customer perception. Prices are carefully calculated in order to achieve the greatest irritation.
Dont ask me why. Its just what they do.
I think you underestimate just how much I just dont care.
Everything should be priced so that everything is divisble by 25 cents so we can get rid of the 1, 5, and 10 cent pieces. I'm all about things getting easier not more difficult.
Just round everything off to the nearest dollar and get on with it -you bean counters!
Also, the US treasury needs to push $1 coins (and perhaps $2 and $5 coins) because the paper money wears out so much faster and costs more to replace than coinage.
Maybe so, but strippers get mad when you try to stuff a $1 coin into their g-strings. Doubly so if you've been holding it up to the bottom of your ice-cold beer.
In walking, just walk. In sitting, just sit. Above all, don't wobble.
-- Yun-Men
The only problem with our current monetary system is that inflation has made pennies freakin worthless.
The penny is a very weird denomination. In Canada anyways, they cost more in materials than they're actually worth, and they don't stay in circulation. It's the only denomination that people would rather store in jars in the basement than spend. Since stores need them to make change, and the coins aren't going back into circulation, the mint has to keep cranking them out due to high demand. It got so bad that at one point, some banks actually paid people .05 cents on the dollar for pennies.
I wonder how much affect this has on inflation, since uncontrolled minting of money usually does cause inflation to go up.
The premise of the paper is that prices like
$3.99 reflect the real value of a good. Does this mean that a
rounding prices upward to the nearest dollar and then subtracting a trivial amount is the custom of american marketers. True or not, american
marketers are convinced that people don't equate
$3.99 with $4.00.
If marketers (american marketers in particular)
dropped this questionable custom, then
denominations.
Since the effifiency of a group of denomiations
is culturally influenced it must also be subject
to change (as does culture) so remaking our coins
would be pretty silly.
lucky you! I recieved nothing but nickels in change for a small purchase with a $10 bill. It hurt when I sat down. :(
Dear god, NO!
We already have 1, 2, 5, 10, 20, 50, 100 and 200 cent coins! Somebody needs to be shot for that. How about a system that aims to reduce the weight of my wallet? 5,10,50,100 seems pretty ideal.
I choose to remain celibate, like my father and his father before him.
That's why the US switched to zinc, since a penny's worth of copper became worth more than 1 cent back in the 70's.
Although I've had situations like yours (giving $11 for $5.xx to get a fiver and change - with curious looks from the cashier), there was one time knowing math really helped speed things for a bunch of people at once.
When a gas station cashier had inadequate change, I was able to figure out how to get myself and 2 other customers to pay, and get exact change back for each of us (I REALLY hate not remembering the numbers) based on the bills we originally possessed. Of course, the cashier still needed more smaller bills for future customers, but it was a temporary fix that satisfied everyone involved. The group was pretty impressed, and (luckily) it was simple enough that they all could follow (everything was in dollars, no cents).
That experience illustrated the one true limitation of a cash machine: strictly focusing on a series of customers (one at a time). If the first customer can't complete the transaction, then everyone behind has to wait until it is complete. Of course, running out of smaller bills can be avoided. I guess they didn't take care of the issue soon enough.
This is not my sig.
How about just saying "fsck it!" and giving a whole $ or 50 cents, and saying that whomever is paid, can keep the change?
It's simpler, better and you both get a nice fuzzy feeling in your gut.
My guess is that the amount of change would be distributed somewhat as predicted by Benford's law. But that's just my guess :)
Pound foolish.
That's gotta fit into your schema somewhere
I was at a Subway, and ordered a twelve inch sandwich. Her reply: "I'm sorry, sir, we only have six inches and foot long."
I'd be curious to see how the average distribution of change is affected by the dominance of Walmart and it's strange method of pricing where most things end up costing X dollars and 88 cents. With the significant percentage of money spent at Walmart, it seems that it would throw off his distribution method, so perhaps a different denomination coin would be more appropriate in dealing with the Walmartization of America.
So that means what? That 83 is not a prime number in Canada?
If Slashdot were chemistry it would look like this:Cadaverine
So you're saying I could help my economy by rolling up my 1KG-sized coffee tin worth of pennies et al. and deposit them to my bank account? Cool! Maybe I can use it to cover the extra cost of a tank of gas nowadays! Everybody wins! ;)
BD Phone Home!
Shameless plug. Like you weren't expecting it.
Change for 48? That'd be two tanners (2 shilling piece, was that their proper name?).
I remember as a child being given sixpence for sweets which, due to decimalisation, was worth 2.5 new pence. I must be getting old because that wasn't a problem seeing as there were plenty of sweets priced at 1/2p.
</old fart mode>
Actually, it doesn't cost more then a penny to produce a penny.
It used to, but then they switched to a cheaper design that was comprised mainly of zinc. In 2000 they changed again, and are now made up mostly of steel
The math is actually very simple, but for some reason, we all try to do it the wrong way. Whether it's some odd flaw in the education system or what, I don't know. Most of us probably start by trying to subtract 37 from 12, which is kind of a pain. The fast way to do this math is to subtract 12 from both figures - this makes everything terribly obvious. For some reason when doing algebra, if you had an equation like this:
x + 12 = y + 2 + 12
most of us would see that we could subtract the 12 from both sides and figure out that x = y + 2.
*sound of my head exploding*
I'm sorry, I can't do algebra...my algebra teacher in college was drop dead gorgeous so x always = cleavage. I think I'll stick to things not so terribly obvious.
The average cachier over the age of 18 barely managed to graduate highschool and is very unlikely to be able to do simple arithmetic. The average engineer I know making $80k+ also cannot do simple arithmetic.
It's hard enough when you have to deal in 5's and 10's, but as soon as you start asking a cachier to add or subtract 18 from ANYTHING, you're going to have trouble.
The whole problem here is that the author doesn't realize that humans are (a) not computers, and (b) don't care about handing out one less coin. The system we have, as imperfect as it is, evolved this way through error and natural selection. Sure, perhaps no one considered printing an 18 cent coin, but that's likely because they knew people would have trouble dealing with them. Humans inherently have trouble with simple arithmetic, so a system evolved that was less ERROR-PRONE, completely ignoring minor improvements in efficiency.
So, of course, one has to ask the question: Could we make the system less error-prone? Probably. Maybe our esteemed computer scientist should develop a system to determine which coins we need to have in order to make it more likely for a cachier to give back correct change.
What's better, taking 2 seconds longer to give you correct change or two seconds less to give you incorrect change? I'll wait the extra 2 seconds.
Or maybe I'll just use my credit card.
Using denominations of 1, 5, 10, and 25, making each change value from one cent to one dollar requires a total of 474 coins (470 if you say that making one dollar requires zero coins).
However, if you knock it back to 1, 4, 10, and 25, you can do it in 430 (426 without the dollar) coins.
Even 1,4,10,20 beats our current system.
Here's the perl code I used to play around with this:This code does almost no input validation or anything like that, though it does force the inclusion of a penny. I have no idea how it'll behave if handed non-integral values.
This code also requires that the coinage system be a "good" system, satisfying criterion 3 of my other post; otherwise, it might overcount the number of coins required.
I'm quite stunned that this guy wrote an _entire paper_ about something that's essentially an optimal golomb ruler computation, and a small one at that.
I suspect another thorn in this plan is that the people handing back change will have serious difficulty in accurately counting out change in those denominations unless the register shows them a little picture of two 18-cent coins, a twenty-seven cent coin, and so on.
I thought the "geek answer" to the problem of making change was an anonymized debit card system.
-JDF
This same system would work even better with paper. Little paper "coins" could be printed on the fly, as needed, in any denomination. If you had to pay $2.41 for something, you wouldn't have to pull out some wierd mix of coins and paper, you just type that into your little money printing maching and print yourself a $2.41 bill!
I've often posited the strategy of rounding prices to the nearest 5 or 10 cent (or even dollar). Most people assume merchants would always rount up, but I argue that any pennies lost rounding down would be more than offset by pennies gained rounding up and labor costs saved by not counting pennies on every transaction. Of course the sales-tax strategy in most states makes the practice exceeding difficult to implement.
I also question the practice of penalizing customers for using debit cards. These charges often range from 25 cents to 2 dollars. My local video store charges a $1 surcharge when renting a $3 video with an ATM card. Until banks and merchants realize that electronic transactions save labor costs, consumers will avoid paying for small purchased with debit cards and my pants will still be weighed down with a pocket full of change.
what about coins of 1, 2, 4, 8, 16, 32 and 64?
;)
Then bills of 1, 2, 4, 8, 16, 32 and 64.
Would make the math lots easier...
What happened to smart cards/credit cards/Embedded chips?
No Change At All!
I hate change.
That's one of the problems with current number systems: they're based SOLELY on what humans relate to easilly rather than a well thought-out system. We have 5 fingers on one hand, 2 sets of hands, feet, eyes, ears, etc. All of a sudden, base-10 and base-2 become our first choice when thinking. I wouldn't be surprised if a lot of concepts haven't been discovered simply because of our predisposition to those number systems.
Anyway, for a 4-coin, sub-dollar system, I still stand by 1-, 3-, 9- and 30-cent pieces since it's not too weird.
...
Now... to take the ferry cost a nickel. In those days, nickels had pictures of bumblebees on 'em. "Give me 5 bees for a quarter!" we'd say.
With the adoption of technologies as CRM, I do not believe that stores consider cost saving when doing customer communication. Unless it is a national campaign, stores usually adapt their prices according to regional competition and the argument of cost savings can not hold.
with denominations that do not divide evenly into each other it is non-trivial to find the optimal change for a given transaction.
What you really mean is "with coinage denomination systems which do not satisfy the greedy choice property, finding optimal change is non-trivial".
As you show, the current US coinage system satisfies the greedy choice property. However, the denominations do not divide into each other evenly. (25 % 10 != 0)
Having denominations divide into each other is sufficient for satisfying greedy choice, but not necessary. [1, 4, 10, 25] also satisfies greedy choice, and there none of the denominations except 1 divide any of the other denominations evenly. (Incidentally, [1,4,10,25] is also an improvement on the current system, in the sense of the paper)
The theoretical employee would just keep a pile of pennies next to the register.
Why is Celil's conjecture any more valid than the other guys?
So what's the real explanation? Having spent two hours poring over the microfilm--no guarantee that I'm not full of BS, but at least it's scientific BS
Casca
In Europe we use 1,2,5,10,20,50.
...
There are more coins but giving back the change
is a lot easier.
Mostly beacuse there is no 25 and you do all
operations on the first and 2nd digit
separately.
Sure, you need more rows in the cash registers
but on the other hand using 50 instead of 2*25
and 2*2 instead of 4*1 is really worth it.
For me this is just another example of
American inability to accept that others
have better system and they should switch.
metric system, Celsius degrees, coins,
cell phones (GSM), paper sizes and so on and so
on and so on
Glad you pointed this out ... you left out the important detail :
Dimes and Quarters are $20 to the pound. You can simply put dimes or quarters (or mix them) on the scale and when you hit exactly one pound, that is $20.
I think pennies are roughly $1.50 to the pound, but that is just a rough approximation.
Glonoinha the MebiByte Slayer
Then we would all be using hex, and non-geeks could understand a binary currency system.
Remember the days when Republicans were the party of fiscal responsibility?
Another post has given criterion 3 the name "the greedy choice property". I like that name, and in the spirit of that name propose the name "the strong greedy choice property" for criterion 4.
There's also another property of coinage systems that might be interesting to look at: that of unique optimal solutions. This is best illustrated by counterexample:
The system [1,4,10,25] satisfies the greedy choice property (but not the strong greedy choice property), but not the uniqueness property, since there are two optimal ways to make 12 cents: 10+1+1 and 4+4+4.
I think that the strong greedy choice property might imply unique optimal solutions.
I'm pretty sure that [1,5,10,25] satisfies the uniqueness property, but I haven't looked at it rigorously.
Why don't stores simply figure sales tax into the equation when setting prices so the total due falls on larger coin denominations. Instead of "$4.99 plus tax", which in my state would be "$5.34 with tax", simply raising the price by 1 cent would reduce the change by 1 coin.
Are there really large numbers of people who think that $4.99 is significantly cheaper than $5.00?
And let's not get into the multi-decimal pricing of gasoline... I know people who burn $1.59 in gasoline simply to save $0.60 on their next 20-gallon fill-up...
To reduce change by 100%, purchase with plastic...
"Obviously, I'm not an IBM computer any more than I'm an ashtray" (Bob Dylan)
I remember from a few days I spent touring Moscow that they have 3 ruble coins there (or at least they did in the early 90s). I was rather clueless about the coins so I would let the merchants help me pick out the coins I was supposed to give them. For some reason, they never took the 3 ruble coins. For the same reason, I don't think that the strange denomination coins in the article would get used very much.
Change:
One $1 bill
One 58c coin
Half this nation can't count past 20 with their zipper up, and this guy expects us to count back change with 18 cent coins?
Counting by 5's, 10's or 25's is easy. The simplicity of accurately counting back the change is more important than the number of coins involved in the transaction.
Good security is based upon reality and common sense. Common sense is a function of having common knowledge.
...Europe has France.
USA wins, hands down.
I am very small, utmostly microscopic.
Here in Canada, we have 1, 5, 10, 25, $1 and $2 coins. Our laundry machine in the basement takes $1.75. Best combination is to use a $1 coin and three 25c coins. To satisfy my quest for always having enough laundry money I end up doing mental arithmetic to get back 25c coins and $1 coins. For example, I get the wierdest looks from teller clerks when I hand them $1.02 when the bill is $0.77. They punch in all the numbers and then get a look of "I see now!!" when the change comes back as 25c. So, this strategy serves two purposes
a) gets rid of loose change from my pant pocket
b) gets enough supply of 25c and $1 coins
Of course, I could go to the bank and get a roll of coins, but then it wouldn't be that much fun, would it?
Corporate Gadfly
Jonathan Archer: the most beaten up Enterprise captain in Star Trek history
I think there's an algorithm big O n^3 for determining whether an n-coinset is greedy operable.
Our change system is not only multiples of 5 because it's easier for a teller to calculate change. But this way, if a teller runs ouf of quarters lets say, well he/she can make it up in nickels and dimes.
If our change system had coins of 18 cents, it would be harder to compensate in the event you ran out of 18 cents. Uhhh I think so!
Where's the love? Come on, now, people. The 18 cent piece is a fine idea. Why, the other day I bought lunch, including a burger and drink, and it came to exactly $4.82. Oh, and it came with fires. I mean, fries. So anyhow, being the smart guy I am, I gave the cashier $7.29, so that the change would be exactly $1.61, which is a nice round number. Easy, but not as easy as the new system. Had the 18 cent piece existed, it would have been even simpler. I could have given her 27 of these new coins and told her that I counted it already, and said it was exact change. By the time she noticed it wasn't, I'd be a mile down the road calling her a sucker. I'd be ahead by at least 4 1/2 cents! Now, which scenario would you prefer, huh?
Why change the coins when you can just as well change the prices? Make all prices end in .00, .05, .10, .25, and include sales tax in the shelf price, and it's very easy to make change.
You see? You see? Your stupid minds! Stupid! Stupid!
All we have to do is issue a US coin for each and every cent amount, from $0.01 to $0.99. Once the mint issues the new coins, the average number of coins to make change in any transaction, assuming an adequate supply of each value of coin, is exactly 1 coin. That beats this mathematical genius's idea by a mile...
*laugh*
18 x some number is just the same as
(20 x number) - (2 x number)
Very!! easy, even for the *stupid* cashier who used his calculator in Jr. High and ruined his mind.
example(7)
7 times 20 is 140. Not hard at all.
2 times 7 is 14. A little trickier but I think most can handle it right?
140 - 14 is also rocket science, but the answer is 126. Some will do it like ( double ((10 x number) - (number)) ) (and this might be even easier), some will do it like ( 20 times number, subtract 1/10 times the value you just got (ie 140/10 is 14).
My point is the math is not really that hard(for the 29 cent it's really trivial, easier than the 18 even). You're doing multiplication with 2s and 3s and the subtraction is the hardest part. Believe me, people will pick this up! There will always be a few who will try and multiply 3 * 18 the *usual* way, but most people will find that it's not that hard. They'll find the simple way to do things because they want to stop having to labour over counting their change and start being lazy again.
As an exercise I leave to you breaking down sums under $1.00 by dividing them by 30 or by 20 and looking at the remainder plus 1*answer or plus 2* answer.
Bring on the funky change!!!
Actually you can throw USA 10, 25, 50, and Large $1 (Ike's and earlier) into a bucket and weigh them. It comes out to $20 per pound. Vegas used to do it this way for years.
I know there have been a couple of Canadian cities that have played with the idea of electronic cash. A large trial was implemented by one vendor, Mondex in Guelph, Ontario a couple of years ago. I'm not sure of the security issues that electronic cash brings to the table, but it certainly would make carrying around cash a lot easier.
In a supermarket, you might end up with a total that includes some small change, but you won't see it - the cashier has a selection of sweets by the till and will, without discussion, drop a chocolate bar in with your shopping, to make the total up to a whole number.
Andrew
More Coins!
I would like to see $5, $10, $20, $50, and $100 coins.
Make them bigger and stronger than the current coins, even print on them with 'color shifting ink' and other protection methods, and put a protective coating on them...
3 or 4 coins in your pocket and you are set for the weekend... Paper money is expensive to keep re-printing, and it is too easy to copy...
Advances in coin technology would be a better method to maintain the money system...
I know it has its benefits, but to me physical currency itself feels horribly outmoded. I use it less and less each year, and I'll be glad when it's a historical curiosity.
org.slashdot.post.SignatureNotFoundException: ewg
Before everyone gets bent out of shape (probably too late), this is just some prof that wrote some paper and submitted it to a journal. In no way is he suggesting that we should all do this.
U Waterloo has some strange people. They take math pretty seriously. I graduated from there a few years ago. I remember at my convocation lining up to enter the gymnasium, we all had a card with a number on it so we would line up in alphabetical order easier. One guy actually announced that his number was prime.
Yes, they're that serious.
Forgive me if this is in the article, I was too lazy to read it, but wouldn't altering the coin denominations then alter the change given distributions? Is he only assuming that things are paid for with whole dollars/euros/etc??
Switching to Linux can be an adventure!
socks and change
In the Soviet days, there were 1, 2, 3, 5, 10, 15, 20 and 50 kopeck coins.
I worked in Russia at the end of the Soviet era for quite some time. One thing I discovered was that I accumulated coins much less rapidly than I did in my native Australia, where change was in the denominations of 1, 2, 5, 10, 20 and 50 cents.
Interestingly, the suggested 18c value falls about half way between 15 and 20. As mentioned in previous posts, multiples of 5 are much easier to count than weird and wonderful numbers like 18.
So it's likely that by design or accident, the Soviets were implementing something along the lines suggested in this study, combined with a little pragmatism about the mathematical abilities of cashiers and the public in general.
You can still find people that do a doubletake when they see a $2 bill, a bill that contrary to popular belief is in circulation and still gets printed, but hardly anyone ever uses, and when someone does get ahold of one, they hoarde it. Retailers will accept them as payment, but they'll end up depositing it and therefore it won't recirculate. Same goes with the dollar coins. Granted, I see them more often than I see $1 bills, but they just don't "fit" anywhere, so they tend to fall into obscurity.
If 18 cent or 29 cent coins suddenly got introduced into circulation, everyone who ran across them would hang onto them. Cash registers wouldn't be redesigned to hold them, so retailers wouldn't stock them or keep a quantity of them around. They'll be out there, they'll be perfectly legal tender, but you'll hardly ever see them, so any hopes of reducing the average number of coins returned in a transaction would probably be better served by a more proactive use of the penny trays.
-Restil
Play with my webcams and lights here
...(which is only every two or three years - I am not the great world traveller) my pockets are always stuffed with coin.
;-)
While very mildly annoying, I suppose it is better than having no money!
Seriously, the 2 and 20 cent coins over there seem to be a waste. Over here, I rearly use the dime.
I am very small, utmostly microscopic.
That was a good little daydream you had there. You might want to consider quitting smoking first and maybe working out a little.
Chances are, the old lady you were trying to beat with that bat would lay you flat with her instinctive purse-flinging.
But your wannabe-violent reaction is certainly indicative of American mentality. I bet the Iraqis tried that change trick on the US and that's the REAL reason for the war.
The point, I think, is that the greedy algorithm fails to provide that solution. Using the greedy algorithm would give a half crown, a shilling and a sixpence.
(btw, according to this page, a sixpence was a tanner, and 2 shillings was a florin.)
I ask this question both with respect to the proposed $0.18 coin (and friends), and with respect to metric time.
The most effective is to use multiples of two.
1,2,4,8,16,32,64 and then either 1.28 or the dollar. Although, the 64 cent piece could easily be skipped. That way, exact change can always be given with as few coins as possible.
But, anyway, it would take serious stupidity to care about what is more efficient. People use monmey, not computers. The current denominations are great for human interaction. Any change would simply be counter-productive.
Have you read my journal today?
I solved this problem back in '95 for a High School Independent study project in Pascal programming. I even tried to get my results published, but didn't get any response from the outlets that I sent them to. I've still got the paper (printed from a wonderful dot-matrix printer)!
Use 1, 3 ,9, 27, and 81 cent coins
Then, as long as any two people have those five coins, you can be sure to have change.
For instance... I owe you 60 cents.
I give you 81, and you give me back 27
I give you 9, and you give me back 3
There are a lot of reasons why this is an interesting mathematical exercise, but really nothing more.
This could clearly result in a reduction in the number of coins needed in circulation. Does anybody have an estimate on what the cost savings to the U.S. Mint would be were this implemented?
How Politicians Lie: http://www.factcheck.org/
"It's the Ningi, not the Pu that you are thinking of. And you got the size wrong."
No wonder I had all of those problems working the cash register at Milliways!
Don't blame Durga. I voted for Centauri.
Eliminating the penny just makes sense.
I know in Europe I always tend to collect pocketsful of 20-eurocent and 50-eurocent pieces. The 1-euro and 2-euro coins are scourge -- as soon as you break a 5 you've got a pocketful of change. I always ended up trying to spend 20 euros of coins at some restaurant.
Hmm, I wonder what people put in strippers g-strings in Europe.
this isn't anythign really new. my combinatorial algorithms prof talked about this almost a year ago. the 1, 5, 18, 29 cent ordeal was a combinatorics question in my book.
has anyone noticed that a uniform distribution was assumed? with most prices ending in x.y9, x.95, i think the uniform distribution might not be very accurate.
Several countries have dispensed with small-denomination coins (the copper ones) entirely to save costs and hassle. For example, in Australia the smallest denomination cash unit is the five-cent piece. Goods are still priced to the cent (or sometimes to a fraction of a cent, e.g. gasoline), but the price for the total basket of goods is rounded down to the nearest five cents. Non-cash transactions (cheques, cards) and bank accounts are still maintained to the cent.
It's a popular scheme, as it doesn't really cost anyone any significant money, bit it saves a lot of pfutzing with small change.
He has an error in his calculations. Try the following program:
a verage = average / (float)(ii-1);
g >
#include <stdio.h>
int main(void)
{
int money = 0;
int ii = 0;
int coins = 0;
float average = 0.0;
for( ii = 1; ii < 100; ii++)
{
coins = 0;
money = ii;
while ( money >= 25 )
{money-=25;coins++;}
while ( money >= 10 )
{money-=10;coins++;}
while ( money >= 5 )
{money-=5;coins++;}
while ( money >= 1 )
{money--;coins++;}
printf("%i change is %i coins.\n",ii,coins);
average+=(float)coins;
}
printf("Average coins per transaction is %f.\n",average);
return (0);}
This gives 4.75 coins per transaction. He must have a fencepost error, because 4.70 coins per transaction is true if you determine that there are 100 transactions, rather than 99 transactions. In my code, that is dividing average by ii-1 (giving 99) rather than ii.
Please excuse the shitty format of the code. Slashdot has a lameness filter. Everything below this post is unnecessary to read, feel free to ignore it.
lalala, typing a bunch of garbage because posting code makes this stupid slashcode shit itself. Oh, no! [b]Your comment violated the "postercomment" compression filter. Try less whitespace and/or less repetition. Comment aborted.[/b] Whatever shall I do? Post some more biting social commentary like I am now? The hideousness! The humanity! Won't someone please think of the children?
Yes, this is totally useless, so I have to post more. And more. And on the seventh day, Taco said, "Let there be lameness filters". And so it was, and much ass was sucked. Ass suckage like was foretold in the holy books.
Should we try it now? Will my completely relevant post that I had to butcher and rape because of this useless filter finally be allowed to post? Stay tuned, same bat channel, same bat time!
Strike 2! What a fucking joke. This bites ass. I just want to post some completely relevant code! That's it! But, no, I can't. I have to keep typing and typing useless shit. Why? We have a lameness filter. Which is working just fine, because I have to add a shitload of lameness just to satisfy it. La la la. This sucks ass. Grrr. I know, let's post a block of useless text from somewhere else! TORONTO - Another round of weak economic news from the United States helped send the Canadian dollar on an upward charge on Friday as it breached 73 cents US.<http://www.cbc.ca/gfx/photos/dollar_030516.jp
The dollar finished Friday at 73.28 cents US, up 0.95 of a cent from Thursday's close. One U.S. dollar was worth $1.3647 Canadian. The loonie's last flight above 73 cents US was on July 14, 1997, when it closed at 73.03 cents US. Friday's close was the dollar's highest since March 12, 1997, when it was worth 73.37 cents US. The Canadian dollar took off after the U.S. Labor Department reported that consumer prices south of the border fell by 0.3 per cent in April. That touched off more speculation the Federal Reserve may cut interest rates in June to spur the American economy.* FROM May 16, 2003: U.S. consumer prices dropped in April The poor economic data coming from the U.S. has sent the greenback plunging this year against many major currencies. The widening gap between U.S. and Canadian interest rates has helped lure investors to buy the loonie. The Bank of Canada has raised rates twice this year to keep control of inflation, while the Fed has left rates at lows not seen in more than 40 years.
"Don't mind me cutting myself on Occam's Razor"
I wonder how much affect this has on inflation, since uncontrolled minting of money usually does cause inflation to go up.
It isn't uncontrolled, so it doesn't have an effect. The Fed doesn't distribute bags of pennies willy-nilly; it gives bags of pennies to banks who give them bills (virtually) in return. Exchanging 100 pennies for a dollar is not inflationary.
I suspect the Fed charges a shipping expense for large coin shipments, and that possibly motivates the penny drives.
On the other hand, coin is profitable for the Treasury (not the Fed): for bills, the Fed only pays the cost of printing the bills, but for coins, the Fed pays face value to the Treasury. Since the coins cost less to make than the face value, the U.S. Treasury gets the profit, called "seignorage." That is one of the main motivations for the state quarter series: a bunch of people (myself included) pay $.25 each for the privilege of getting a stamped piece of metal, which we will never return to circulation. Most quarters eventually wear out enough that the Treasury has to eat the cost when the Fed returns them. Not so if they spend the indefinite future in a box!
One big flaw in his analysis is that he uses the averages of a number of purchases to determine the efficiency of various denominations. The problem with this is that prices change over time. You cannot constantly come out with new denominations to chase after price flucuations, it would cause chaos. The best coins for today may not be the best 5 years from now. The best thing to do (and we do it now) is to set a standard based on the base 10 system.
His other major error is his very definition of efficiency. The number of coins handed out is a small part of the transaction's total time, the biggest part is the time needed for the cashier to add up the change or the customer to add up their payment. Sticking to units of 5 makes addition in your head a hell of a lot easier than, say, 6, 7 or 8. I agree with the parent comment, can you imagine someone trying to add multiple 18 cent pieces during the lunchtime rush?
This whole article strikes me as nothing more than a mathematical recreation that has been used for self-promotion.
It is by the juice of the coffee bean that thoughts acquire speed, the teeth acquire stains. The stains become a warning
Wouldn't the solution vary from state to state (or even city to city) depending on the sales tax collected?
So, rather than adding an 18-cent piece, did he look at what would happen if prices were rounded off to $0.05 increments instead (in the US, at least)?
Does the whole thing satisfy the axioms of matroids?
...)
I was just wondering if someone can give the answer (I do not know, it's late now, I can't think about it, but if the greedy algorithm works
The only denominations of currency should be prime numbers greater than 50, but there will be many things charged in all numbers from 1-50. That will give people's brains a workout so they don't decay from lack of use. Or at least it will make handing out change fun.
Has anyone noticed that Canadian coins look suspiciously like their US equivalents? Sometimes, you can fool Americans into accepting Canadian coins (which are worth less), and on just about every bus I've tried it on, their coin-slots will accept Canadian coins. I have a conspiracy theory that the Canadians are waging economic warfare against the Americans by trying to replace the US currency with the worthless Cnaadian currency, and therefoe reducing the value of the US economy.
If you get rid of the penny, I'll bet the average number of coins also drops dramatically!
Boy, I wish my country did this, too.
Not only for the hexadecimal counting, but think of the emacs key combinations we could create! We could double or triple what we have now (this is eight fingers PER HAND right?)
In New Zealand, we did away with 1 and 2 cent coins some time ago. This means all 'real' cash transactions are multiples of 5 cents (e.g. $9.95) and giving change is pretty straightforward and requires less mathematical 'effort'. We use the 'swedish' (or was it 'swiss'...) rounding system where products aren't priced like this (e.g. in supermarkets) to convert to the nearest 5c multiple.
:) New Zealand was the first country in the world to introduce it (twice in fact) and we've never looked back (well, except that first time...)
For 'virtual' cash like credit card, EFTPOS cards, etc, the value is not rounded and the exact price is paid via the electronic point-of-sale terminal. Same with cheques I think, but with the advent of EFTPOS, cheques are becoming very rare for daily transactions.
BTW, if your country doesn't have EFTPOS yet, you're missing out
As I am sure many people have pointed out, the 1.33- or 1.37-Euro coin already exists.
It's called the pound coin
Happy to have helped.
My bank charges a transaction fee for using my debit card.
My plan gives me 10 free transactions a month, one is to pay my credit card.
The acronym or the explanation...
:-)
I think its much more likely that someone began calling them bits, and then coined the acronym explanation aftewards. (BTW. is it BInary digiT, Binary dIgit og Binary digIT?)
Hey I have this simple programming language I'm thinking of calling "Beginners All-purpose Symbolic Instruction Code"... Hey what a funny coincident! That spells "BASIC". How convenient.
In Canada anyways, they cost more in materials than they're actually worth
That's not true any more. Around 1997 or so they switched from making copper pennies to using electroplated zinc.
You can easily tell when they switched once you know what your looking for.
A way to keep the minimum amount of coins in your pocket and still have the correct change for any occasion is to keep each denomination that will make up one less coin than the higher denomination. For example one quarter requires two dimes and one dime requires one nickel and one nickel requires four pennies. In Canada I always try to carry the following:
* 2 - two dollar coins
* 1 - one dollar coin
* 3 - quarters
* 2 - dimes
* 1 - nickel
* 4 - pennies
Oops. I forgot that slashdot would think the amounts in angle-brackets were HTML tags, rather than straight text. Let's try that example again.
Example: $1.33 sale from $20
one thirty three.
(penny) [one] thirty four
(penny) [one] thirty five
(nickel) [one] forty
(dime) [one] fifty
(quarter) [one] seventy five
(quarter) two dollars
(dollar bill) and three
(dollar bill) and four
(dollar bill) and five
(five dollar bill) and five makes ten
(ten dollar bill) and ten makes twenty
Bantam Dominique roosters crow a four-note song. Once you've heard it as "Happy BIRTHday" you can't NOT hear it that way
The math is easy, it reduces the number of denominations, and results in virtually the same number of average coins at the 18 cent piece.
Also, with only 4 types of coins, it makes for extra room in cash drawers, few coins types to reconcile, and the math is within the bounds of the average person.
The same advantage accrues in currency also.
In spending only bills and receiving change, we deplete the vendor's supply of change, while we become heavy with change as we shop. This is unrealistic. A slightly different problem is to try to minimize the total number of coins that pass back and forth where I give the cashier change, and he returns me change:
choose the 4 coin demoninations P, N, D, Q such that for a value R between 0 and 99,
i*P + j*N + k*D + l*Q == R % 100,
where abs(i) + abs(j) + abs(k) + abs(l) is minimized over all random R.
For instance, if the price is $.29 cents, rather than spending $1 and receiving 2 quarters, 2 dimes, and a penny (5 coins), I spend 1 quarter, 1 nickel, and receive one penny (3 coins).
I need some stability!
Naturally, discarding negative coins would have to be made a crime, like littering, but worse. Enforcement could be combined with the solution to another problem. As other posters have mentioned, cashiers would have problems with odd coinage systems. Cash registers would have to tell the cashier exactly what coins to return.
Since the registers are counting the individual coins, they might as well track which customer the coins are given to and report this to the government. Then the government can audit each citizen to ensure their negative coins are accounted for and have not been thrown out a car window somewhere. Slashdot participants will appreciate the value of this scheme immensely.
Also, the article considers only minimizing coins that form a transaction value. However, the cost of a coinage system is not just in how many coins are returned when you pay with whole dollars but in how many coins are exchanged in a transaction and how many coins are carried around. E.g., I am not just going to accumulate coins. At some point, I will give the cashier not whole dollars but dollars and coins. What coinage system minimizes the total exchange?
More generally, suppose there is a cost x per coin exchanged (time to count and hand over, etc.), a cost y per coin carried in a pocket (calories, emptying pockets at home, adding to compute time when deciding what to give to cashier, etc.), and a cost z per coin carried in a cash register (time to get stock from bank, to return stock to bank, to count at end of day, etc.). What coin system minimizes the total cost?
Perhaps someone should have done their research first. Although you may not see the 50cent piece much, you can get it at any bank, and the local postage-stamp machine always returns them.
Malachi
http://www.google.com/profiles/malachid
Life gets more complicated when coming originally from Germany, where VAT is always included in the advertized price (for end-users, not for businesses) and going to Japan, where 5% tax is mostly added. About 90% of all times I need to add 5% at the cashier. In the other cases I don't need to. Now that makes calculation the price to pay complicated.
I wasn't trying to imply that math majors should be able to do arithmetic in their heads. I was using that example to illustrate that I'm aware that mathematical knowledge and the ability to do calculations in one's head are separate things. And that I wouldn't assume that because one cannot do math in one's head, it doesn't imply that they aren't smart, or don't understand mathematics.
My original point wasn't about doing math in one's head. It was that the other person seemed to be unaware that doing a (simple) calculation like that was even a possibility. I was using my wife as the example that even though she might not do something like that in her head, that she would recognize that it is entirely possible that someone could.
I would guess that eliminating pennies would make at least as big a difference in the number of coins required to make change as using 18c coins. Let's find out:
.05 = 1 .10 = 1 .15 = 2 .20 = 2 .25 = 1 .30 = 2 .35 = 2 .40 = 3 .45 = 3 .50 = 1 .55 = 2 .60 = 2 .65 = 3 .70 = 3 .75 = 2 .80 = 3 .85 = 3 .90 = 4 .95 = 4
Assume any amount of change between $.05 and $.95 is equally probable.
Assume nickels, dimes, quarters, and half-dollar coinage:
The average is 2.315 coins per amount.
Of course, there would be a cost in terms of economic efficiency. Stocks could only move by $.05 per share at a time, etc. Over billions of transactions, the missing "resolution" that pennies provide would make make financial markets far less liquid.
At the retail level, however, it would probably save 10 to 15 seconds every time someone paid cash.
Amazing magic tricks
If they think your method is "magic", just imagine their reaction to this scenario:
:)
$20 tendered for $1.33 sale
(ten dollar bill) leaves ten
(five dollar bill) five
(dollar bill) four
(dollar bill) three
(dollar bill) two
(quarter) [one] seventy five
(quarter) [one] fifty
(dime) [one] forty
(nickel) [one] thirty five
(penny) [one] thirty four
(penny) one thirty three.
Ok, I have an evil and twisted sense of humor
-
- - You can't take something off the Internet! That's like trying to take pee out of a swimming pool.
Joe Ganley
http://ganley.org/
True, ours in Virginia should be $1.03455 (VA sales tax is only 4.5%). I guess we could call it a "sales tax friendly" coin.
Pedro
----
The Insomniac Coder
If non-cash transactions took place using Penny amounts, how would they be reconciled? Sure they could exist, but at the moment when they were reconciled they would need to be rounded.
The knowledge that the pennies would eventually be rounded to the nearest nickel would result in investors making decisions based on the nearest nickel.
Also, both the NYSE and the NASDAQ have been using decimal values for stocks for the past couple of years.
Amazing magic tricks
Who actually uses cash beyond feeding a vending machine? You want to make change more efficiently? All the cool kids use plastic. No thinking required for anyone.
Florin! Right you are (this was all slightly before my time anyway).
Anyway, getting rid of the penny would be just the thing to save the dollar coin. Consider how most people get coins: they receive them from merchants as change. Merchants don't like stocking more than 4 kinds of coins, which is why nobody uses half-dollar or dollar coins.
(Yes, we (the U.S.) have half-dollar coins! Haven't even seen one for years. They're too big for vending machines, as were the old Eisenhower dollars. But they're still available.)
If we did away with pennies, that would make room in the cash registers for dollar coins. Having those would make it a lot easier to pay transit fares, tolls, and to buy those overpriced soft drinks everybody guzzles.