2002-01-02 13:47:04, "Ma Be" <[EMAIL PROTECTED]> wrote: >On Tue, 01 Jan 2002 16:16:39 > Daniel Bishop wrote: >... >>The US did have a 20 cent coin at one point. There's an article about it at >http://www.coin-gallery.com/cgmarotta.htm . >> >Interesting... Why didn't they stick with that though? > >>btw, I'd like to know where you found this proof that a 1, 2, 5 system is more >efficient than 1, 5, 10, 25. >... >That's actually quite easy to derive. You could do it yourself. This is based on >the assumption, evidently, that the universe of prices follow no... "preference" for >any >particular value. I.e. that it's just as probable for one to find a value of, say, >0.35 $ or .87 $ in the market. This assumption is important because if there were any >particular values that would occur more often or something like that it would >unfairly skew the analysis towards a specific system. Nonetheless, it stands to >reason >that overall 1,2,5 primes would work much more efficiently. > >The basic assumption I'm making for efficiency is that one would require a >significantly lower amount of coins to express any cent value. This is how you'd do >it. > >Derive a table of the most efficient way to provide changes for values from 0.01 >cents to 0.99 cents (here another parenthesis to comment that one is assuming that people would conduct changes in the most efficient way possible most of the time, which may not be the case. For instance, for a 45 cent change one would provide 2 x 20 + 2 x 2 + 1 - 5 coins, instead of 4 x 10 + 5 x 1 - 9 coins! - and any another possible combination, if you know what I mean. Please remember that I'm debating efficiency here!) using 1,2,5 prime-designated coins. Now do the same with your present system.
I did the math myself, and here's what I found: With coins worth 1c, 5c, 10c, and 25c (the current US system), the average number of coins given in change is 4.7. With the 1,2,5 system, only 3.4 coins are required. If coins under 5c were eliminated from both systems, then this average would be 2.7 coins in the US system (2.2 if the 50c coin were used) and 2.2 coins in the Euro system.
