As soon as I read "But you will have five too many chestnuts if I gave you one chestnut more [than five]", I figured that this has to do with modulus 5 arithmetic, where 6 = 1. So my solution is based on that idea.
Answer: For 3 twenty dollar bills, the man should have gotten 15 chestnuts. (That doesn't sound very equitable, but hey, this is a "nonsense puzzle" !!)
Explanation:
Whenever a shopper hands the shopkeeper a bill which is the equivalent of N dollars (N=1 for a dollar bill, N=5 for a five dollar bill,...,N=20 for a twenty dollar bill, ...), the shopkeeper gives F[N] chesnuts to the shopper, where
F[N] = 1 + [(N+4) mod 5]
But when the shopper in the puzzle came in, the shopkeeper accidentally typoed the function:
G[N] = 5 + [(N+4) mod 5]
So the shopkeeper handed him
G[1] = 5 + [(1+4) mod 5] = 5 chesnuts.
Realizing that a mistake had been made, the shopper asked for an extra chestnut, for a total of 6. But the shopkeeper realized that the correct number should be F[1] = 1 + [(1+4)mod 5] = 1 chestnut, so he knew that 6 would be 5 too many. Hence his answer.
Now F[20] = 1 + [24 mod 5] = 5
So each twenty dollar bill should get him 5 chestnuts. Three twenty dollar bills will therefore get him 15 chestnuts.
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Posted by Penny
on 2004-01-06 00:09:00 |
Solution
