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?

Of course, we were lucky to determine Harry's coins in just two questions.  His coins "catered" to the questions that we asked.

Because there are only 8 combinations, three yes-no questions can be devised that will always determine his coins.  

(Coincidentally, there are 8 coins)

Coincidentally, each of the coins  is in exactly half of the 8 combinations, so there are a very large number of simple questioning schemes that will work.

For instance, one simple scheme would be to ask if Harry has a 1p coin, and then ask if he has a 200p coin.  No matter what he answers, we have eliminated all but two combinations, and one more question which tell us which one.

Posted by Steve Herman on 2005-09-17 12:23:27