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Two sets of Coins (Posted on 2005-10-07) Difficulty: 2 of 5
You have two sets of five coins. Each set has four real 30g coins and one 31g fake coin. It is easy to find the fake coins using a balance scale a total of four times, two weighings for each set.

Can you find a strategy which uses only three weighings?

  Submitted by Brian Smith    
Rating: 3.5000 (2 votes)
Solution: (Hide)
Label the coins from the first set of five A,B,C,D,E and the coins from the second set F,G,H,I,J. Weigh ABCF/DEGH.

If ABCF>DEGH then one of A,B,C is a fake and one of F,I,J is a fake. Weigh A/B and I/J to determine which.

If ABCF=DEGH then the fakes are (AG),(AH),(BG),(BH),(CG),(CH),(DF), or (EF). Weigh G/H.
If one of G or H is a fake then one of A,B,C is the other fake. Weigh A/B to determine which.
If G=H then F is a fake and one of D and E is a fake. Weigh D/E to determine which.

If DEGH>ABCF then one of D and E is a fake and one of G,H,I,J is a fake. Weigh DG/EH.
If DG>EH then D is a fake and one of G,I,J is a fake. Weigh I/J to determine which.
If EH>DG then E is a fake and one of H,I,J is a fake. Weigh I/J to determine which.
If DG=EH then either D and H are the fakes or E and G are the fakes. Compare the two pairs to determine which.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Dum solutionDeep,Dark&Dummy2006-01-10 06:33:09
Solutiontwo sets of coinsDeep,Dark&Dummy2006-01-09 06:16:23
re: not sure i get your logic for scenario two...Charlie2005-10-21 14:01:06
not sure i get your logic for scenario two...Mad2005-10-21 00:23:43
SolutionsolutionCharlie2005-10-07 21:48:39
Hints/Tipsre: 3 simple stepsCharlie2005-10-07 18:57:24
Solution3 simple stepsAdy TZIDON2005-10-07 16:15:03
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