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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?

  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.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some Thoughtsre: answerAdy TZIDON2015-01-09 23:54:13
answerK Sengupta2007-09-12 01:15:55
My take on what Harry;s gotRich2005-11-12 15:36:46
re: question about problemmonica2005-09-21 04:48:53
Questionquestion about problemmonica2005-09-21 04:04:11
re: Coincidence and binary searchesSteve Herman2005-09-18 12:52:54
re: Errata: 1st solutionSteve Herman2005-09-17 15:58:04
Errata: 1st solutionPercy2005-09-17 12:47:33
Coincidence and binary searchesSteve Herman2005-09-17 12:23:27
Variation on the puzzlePenny2005-09-17 12:16:05
SolutionSolutionBractals2005-09-17 04:19:51
SolutionSteve Herman2005-09-17 03:33:17
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