All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Two sets of Coins (Posted on 2005-10-07)
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.

 Subject Author Date Dum solution Deep,Dark&Dummy 2006-01-10 06:33:09 two sets of coins Deep,Dark&Dummy 2006-01-09 06:16:23 re: not sure i get your logic for scenario two... Charlie 2005-10-21 14:01:06 not sure i get your logic for scenario two... Mad 2005-10-21 00:23:43 solution Charlie 2005-10-07 21:48:39 re: 3 simple steps Charlie 2005-10-07 18:57:24 3 simple steps Ady TZIDON 2005-10-07 16:15:03

 Search: Search body:
Forums (0)