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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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Coincidence and binary searches | Comment 4 of 12 |
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
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