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Divide into Primes (Posted on 2005-09-17) Difficulty: 3 of 5
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?

See The Solution Submitted by Charlie    
Rating: 3.2857 (7 votes)

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Solution Solution | Comment 2 of 12 |
 
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
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