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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.

18 of 935 comments (clear)

  1. I hate math... by Swannie · · Score: 5, Funny

    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!
    1. Re:I hate math... by Khasmo · · Score: 5, Insightful

      Beyond that, it also means the cashier would have to figure out what the most efficient combination of change is . . for 0.36 don't give a quater two nickels and a penny, just give two 0.18 coins.

      The logic for determining change is really easy for a cashier. start with the largest coin and work your way down until it all adds up.

  2. Yeah Right... by IpsissimusMarr · · Score: 5, Funny

    Are you kidding me?!

    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, ... *pause* .... and just stare blankly at the change drawer.

    --
    "Engineers do the work of man, Physicists do the work of God"
    1. Re:Yeah Right... by ip_vjl · · Score: 5, Funny

      One time at a grocery/conveneience store, I had a total come to something like $1.87

      Wanting to minimize some of the change in my pocket, I gave the clerk $2.00 in bills and 12 cents.

      The clerk tried to hand it back, saying "it's only $1.87"

      I said, "yes, but this way, I'll get a quarter back in change."

      He took the money, punched it into the cash register, and as he handed me back the quarter, he said "How did you know that?"

      It's funny (in a VERY sad way) that to him, the cash register was this magic oracle that told him what to do, and that it didn't occur to him that what he was doing was even knowable without its use.

    2. Re:Yeah Right... by gentgeen · · Score: 5, Insightful

      It's funny (in a VERY sad way) that to him, the cash register was this magic oracle that told him what to do, and that it didn't occur to him that what he was doing was even knowable without its use.

      I am a High School math teacher, and I can't agree with this statement enough. Somedays I laugh, somedays I cry, but it is always sad when I see a student need the calculator for the most BASIC of operations (And I am not even counting the OP's example as "basic", that would be "basic+")

      I think it all comes from the fact that students are allowed to use calculators at such an earlier point in thier schooling. I am only 29, but I was not allowed to use a calculator in school until somewhere around 11th grade. It really hones (sp?) those basic math skills. I'll step off my soap-box now Sorry ;-}

    3. Re:Yeah Right... by ip_vjl · · Score: 5, Insightful

      I don't blame people for not being able to do math in their head. I know some smart people that have trouble doing calculations without paper. My wife was a math major in college, and she sometimes has problems doing calculations in her head.

      The thing that struck me about this guy was that it wasn't even that he couldn't do the math in his head ... he wasn't even aware that there was something that he could do to arrive at the answer. It's as if he didn't know that math even existed.

  3. Instead... by frodo+from+middle+ea · · Score: 5, Insightful

    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".
    1. Re:Instead... by jmv · · Score: 5, Informative

      In France (and probably other countries) most of the prices end in .00 and the taxes are already included (unlike Canada where I live). It's much simpler that way. If only there was a way to convince stores to do that in here...

    2. Re:Instead... by GospelHead821 · · Score: 5, Insightful

      They're not trying to fool anybody. At least, that was not the original intent of setting prices at $9.99 instead of $10.00. It was a technique that was intended to help keep cashiers honest. If an item cost exactly $10.00, the cashier didn't need to open the drawer to get change for the customer. At some point, it was determined that cashiers who did not have to open the drawer were statistically more likely to pocket the money themselves than to put it in the register. So prices were dropped by a penny to force the cashier to open up the cash drawer, to get change for the customer, thus increasing the statistical likelihood that company gets its money.

      --
      Virtue finds and chooses the mean.
      Aristotle, Ethica Nichomachea
  4. The quarter is hard enough by charlieo88 · · Score: 5, Funny

    I was at a conveinece store yesterday. The price came to $1.37. I tendered $2.12. The cashier's head almost exploded.

  5. Yeah, right... by Frightened_Turtle · · Score: 5, Funny

    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!
  6. Science v. Common Sense by MilesParker · · Score: 5, Interesting

    More proof of the ungoing schism between science and common sense.

    Me, I'm on the side of science.

  7. 18, it's a magic number. by MexicanMenace · · Score: 5, Funny

    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.

  8. Preposterous by syle · · Score: 5, Funny
    An 18 cent coin is a good idea, but it's only a start. What we really need is one coin per possible amount of change. That way, when you pay with $1.00 for a $0.63 candy bar, you just get one 37-cent coin in return.

    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

  9. why did we ... by da5idnetlimit.com · · Score: 5, Interesting

    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
  10. Re:Forget it. by omega_cubed · · Score: 5, Informative
    Quoth Terry Pratchett and/or Neil Gaimen (as they coauthored, and I have no idea which came up with this) in Good Omens:
    NOTE FOR YOUNG PEOPLE AND AMERICANS: One shilling = Five Pee. It helps to understand the antique finances of the Witchfinder Army if you know the original British monetary system:

    Two farthings = One Ha'penny. Two ha'pennies = One Penny. Three pennies = A Thrupenny Bit. Two Thrupences = A Sixpence. Two Sixpences = One Shilling, or Bob. Two Bob = A Florin. One Florin and one Sixpence = Half a Crown. Four Half Crowns = Ten Bob Note. Two Ten Bob Notes = One Pound (or 240 pennies). One Pound and One Shilling = One Guinea.

    The British resisted decimalized currency for a long time because they thought it was too complicated.
    --
    Engineers also speak PDE, only in a different dialect.
  11. 5?! -Interesting +Utter Crap by Anonymous Coward · · Score: 5, Informative

    Cecil has the right answer instead of this complete conjecture.

  12. A "Scientist" wrote this!?!?!?!? by radulovich · · Score: 5, Insightful

    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.

    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/ne ws_and_views/straight_dope.html)

    - 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/ne ws_and_views/straight_dope.html)

    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