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How many coins can five weighings handle?

weighingternaryinformationgeneralisation

A pile of coins contains exactly one coin that is heavier than all the others, which are identical. You have a two-pan balance and are allowed exactly five weighings.

What is the largest pile size for which you can always find the heavy coin? Explain why one more coin would break your method, no matter how clever it is.

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Work backwards from the last weighing. How many coins can a single weighing search? Then how many can two? Look for the pattern.

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Balance-Scale Weighing ProblemsOptimal Card Guessing When You Count What Is GoneHat-Colour ProblemsSigma-Algebras and FiltrationsAdaptive Versus Pre-Committed Weighing Strategies

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