We are working on the logic problem from IMP Level 1 entitled "Twelve Bags of Gold". We can solve the problem when the first weighing is equal, but if it is unequal we get too many weighings. FYI: the problem states that a king wishes to find the one bag of counterfeit gold out of his 12 bags; he has only a pan balance scale and wants to do it in 3 weighings. He does not know if the counterfeit gold is heavier or lighter than the real gold. Are you familiar with this problem? We have found it very interesting, and have been working at it for a week now. Would appreciate any guidance that you can give. Thank you, C.

(Remark. This problem is often stated as the "Twelve Coins" problem: you are given twelve coins, eleven of them fair and one false, and asked to use three weighings on a balance scale to find the false coin and tell whether it is heavy or light. We'll call this the Odd Weight Coin Problem. If you know in advance whether the false coin is heavy or light the problem is simpler; using n weighings you can distinguish the false coin among 3ⁿ coins; for example, with 3 weighings you can distinguish a false coin among 27 coins instead of only 12. We'll call this the Known Weight Coin Problem. If you're not familiar with this simpler problem, you should study it first. It is written up as another Best of MathNerds item here: The Counterfeit Penny.)

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