Fake Coins Puzzle: A, B, C, D, E, F, G, H, I, J Divide this up in two grps First Use of Balance: Weigh ABCDE vs FGHIJ Two possibilities, weghts are the same and weights are different. 1. If Weights are the same for the two grps, ie. ABCDE = FGHIJ There is a fake coin on each group. For each grp; ABCDE and FGHIJ make a sub grp of two coins X 2 and 1 coin, eg. AB, CD and E for ABCDE Second Use of Balance: Weigh AB vs CD, if they weigh the same E is fake. if AB < CD, then A or B is fake Third Use of Balance: Weigh A vs. B, whichever is less, it's fake. Repeat the same for FGHIJK. The max use of balance is 5. 2. If ABCDE < FGHIJ then ABCDE has both fake coins. Divide into sub grp of 2 coins X 2 and a single coin, like AB, CD and E Second Use of Balance: Weigh AB vs CD, if they are both equal, both of them have one fake each. Then weight A vs B and C vs D. Smaller weights are fakes. (Total number of balance use 4) If AB < CD, then AB must contain at least one fake, weigh A vs B. If A=B, then they are both fake. (total number of balance use = 3) If A

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