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!
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"
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".
I was at a conveinece store yesterday. The price came to $1.37. I tendered $2.12. The cashier's head almost exploded.
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!
More proof of the ungoing schism between science and common sense.
Me, I'm on the side of science.
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...
I'm waiting to see if Taco screws it up in the dup tomorrow, too...
MDC
Do you have ESP?
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?
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.
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
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
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.
Engineers also speak PDE, only in a different dialect.
Some egghead thinks "optimal" means "fewest coins returned in change, on average."
/. to come along and rip everything out of context.
No no no. Academia don't have to think about definitions. We just define it that way.
Be seriously, RTFA, people. The important part of this result is not that 18 or 83 cent recommendations. The author did it in jest in reference to the phrase "What this country needs is a good five cent cigar". (cited in the footnote of the paper). Just wait for
The important part of this paper is the second half, the general analysis of methods for finding "optimal" denominations or "optimal" change returns (the first defined to minimize the number of coins returned on average, the second defined as given a set denomination, finding the best way to represent a given amount). It gives asymtotic results. It is more of a computer science excercise then anything else.
W
Engineers also speak PDE, only in a different dialect.
There's another problem. Quote from the ScienceNews article:
Assuming that each amount of change between 0 and 499 cents is equally likely, Shallit's calculations show that the average cost of making change would fall from 5.90 to 4.58 coins per transaction with the addition of an 83-cent coin.
That's a pretty big assumption, isn't it? I'd assume that amounts of change would cluster around certain values. That was one thing that caught my interest, so I went to look at the article to find out how they evaluated that effect. Answer: apparently they didn't.
To be fair, it's quite possible -- even probable -- that the original article was a light-hearted, tongue-in-cheek sort of piece, and that the author has been horrified to see it turned into a serious suggestion about actually changing the denominations of coins.
In fact, the more I think about it, the more likely this seems. From TMI's site: "The Mathematical Intelligencer encourages authors to write in a relaxed, expository style and to include pictures and other graphics with articles. Opinion, mathematics, and historical comments can (and often should) be intermingled to make lively reading. Humor and controversy are welcome." So it was probably just a goofy abstract problem, written for entertainment value, not "serious" research. So I take it all back: let's give the guy a break, smile quietly, and move on.
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
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
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!
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
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.
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