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?

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