The coins currently in circulation in Britain are for 1p, 2p, 5p, 10p, 20p, 50p, 100p and 200p. When I gave one of each of these coins to Tom and Harry to share between them, each took two or more coins, with each person's coins' total value equal to a prime number of pence. No coins were left over.

I asked Harry whether his share was a specific number of coins that I mentioned. He said "no".

I then asked Harry whether he had the coin of a denomination I specified. He said "yes".

His two answers allowed me to determine the total of the value that Harry had taken. What was that value?

A Perl program gives the following eight possible sets for Harry:

  #   1p    2p    5p   10p   20p   50p  100p 200p      Total

  3    X                       X     X                   71p  

  3    X                             X          X       251p

  3          X     X                       X            107p

  4    X                 X     X           X            131p  <==

  4          X     X                 X          X       257p  

  5    X                 X     X     X          X       281p

  5          X     X     X     X           X            137p

  5          X     X     X                 X    X       317p

Harry did you take five coins? No.

Harry did you take the 10p? Yes.

Harry you have a total of 131p.

Posted by Bractals on 2005-09-17 04:19:51