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Brainteasers

Find the heaviest of eight with a balance

weighingcomparisonstournamentlower-bound

You have eight coins, all of different weights, and a two-pan balance. You may only compare one coin against one coin at a time; the balance tells you which of the two is heavier.

What is the minimum number of comparisons that guarantees you identify the heaviest coin? Prove that no cleverer scheme can do better.

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Think of each comparison as a match in a tournament: one coin "loses". How many coins must lose at least once before you can be sure who the champion is?

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