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 Divide into Primes (Posted on 2005-09-17)
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?

 Submitted by Charlie Rating: 3.2857 (7 votes) Solution: (Hide) The coins add up to 388 pence. The possible values that add up to 388 pence, and the divisions of the denominations, are: ``` 5 383 5 vs 1,2,10,20,50,100,200 29 359 no way 41 347 no way 71 317 50,20,1 vs 2,5,10,100,200 107 281 100,5,2 vs 1,10,20,50,200 131 257 100,20,10,1 vs 2,5,50,200 137 251 100,20,10,5,2 vs 1,50,200 149 239 no way 191 197 no way ``` Since each of the two took more than one coin, 5+383 is out. Some values split between 3 coins and 5 coins, while 131+257 splits into four coins on each side. If I had asked if the number of coins was 4, and received that negative answer, then no matter what denomination was confirmed, there'd be more than one possible value that Harry could have. Likewise if I had asked if the number of coins was 3, then no matter what denomination was confirmed, there'd be more than one possible total among the 4 and 5 coin sets. If you look at the numbers, you'll see that the 10p denomination is never part of a group of three. So if I had asked if the number of coins was 5, and received a no answer, and then asked if he had taken the 10p piece and the answer was yes, it would have to be the 4-coin set that contains the 10p piece, and that has a value of 131 pence. This is New Scientist's Enigma # 1346 from the issue of 25 June 2005.

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 Subject Author Date re: answer Ady TZIDON 2015-01-09 23:54:13 answer K Sengupta 2007-09-12 01:15:55 My take on what Harry;s got Rich 2005-11-12 15:36:46 re: question about problem monica 2005-09-21 04:48:53 question about problem monica 2005-09-21 04:04:11 re: Coincidence and binary searches Steve Herman 2005-09-18 12:52:54 re: Errata: 1st solution Steve Herman 2005-09-17 15:58:04 Errata: 1st solution Percy 2005-09-17 12:47:33 Coincidence and binary searches Steve Herman 2005-09-17 12:23:27 Variation on the puzzle Penny 2005-09-17 12:16:05 Solution Bractals 2005-09-17 04:19:51 Solution Steve Herman 2005-09-17 03:33:17

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