Six Coins, One Honest Scale
Six coins are laid out. Each one, independently, is either genuine (10 g) or counterfeit (9 g), so any pattern from all genuine to all counterfeit is possible. You have a digital scale that reports the exact total weight of any collection of coins you place on it. Weighings may be chosen adaptively, based on earlier readings. What is the minimum number of weighings that always suffices to determine, for every coin, whether it is genuine or counterfeit?
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Source: Adaptive variant of the coin-weighing problem posed by Soderberg and Shapiro (1963). Statement written for AxiomIQ.