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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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Variation on the puzzle | Comment 3 of 12 |

If the answer to the second question ("I then asked Harry whether he had the coin of a denomination I specified"), is "No", then the questions were:

 "Do you have 3 coins ?" ("No") 

"Do you have a 10p coin ? ("No").

Then Harry could only have had 257p total {2p, 5p, 50p, 200p} 

[If Harry didn't have 3 coins, then his only possibilities were:

{1p  10p  20p  100p  (sum = 131)}
{2p  5p  10p   100p  200p  (sum = 317)}
{2p  5p  10p  20p 100p (sum = 137)}
{1p  10p  20p  50p 200p (sum = 281)}
{2p  5p   50p  200p  (sum = 257)}  ] 



Edited on September 17, 2005, 12:19 pm
  Posted by Penny on 2005-09-17 12:16:05

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