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.

Comments

Re:Instead...

[jmv]

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...

Re:Forget it.

[omega_cubed]

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.

Re:This is why Human Interface Design is important

[omega_cubed]

Some egghead thinks "optimal" means "fewest coins returned in change, on average."

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 /. to come along and rip everything out of context.

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

5?! -Interesting +Utter Crap

[Anonymous Coward]

Cecil has the right answer instead of this complete conjecture.

Re:Instead...

[simong_oz]

In Australia copper coins (1c & 2c) were taken out of circulation in 1991 (I think). So everything is rounded to a multiple of 5c. The rules for the rounding (set out by law) are:

For cash transactions:
1 & 2 cents -- rounded DOWN to the nearest 10 cents
3 & 4 cents -- rounded UP to the nearest 5 cents
6 & 7 cents -- rounded DOWN to the nearest 5 cents
8 & 9 cents -- rounded UP to the nearest 10 cents
Rounding is on the total value of the bill. Individual items should never be rounded.

And where a consumer pays by cheque, credit card or EFTPOS (electronic transaction) there is no need to round at all.

So basically you win some and you lose some, but it evens out in the end. If you're really diligent, yes you can use it to your advantage, but most people have a life instead.

Re:Pirates

[Martin Blank]

Almost. The piece of eight (the Spanish Milled Dollar, worth eight reales) was one of the principal coins of the colonies, but the coin was not broken up. Instead, coins of values equivalent to one-half, one-quarter, and one-eighth of a dollar. One piece of eight was worth on real, eight reales to a dollar...

And now you know.