The scale that only says equal or not equal
You have eight coins, one of which is heavier than the other seven. Your balance is faulty: a bell rings when the two pans hold exactly equal weight, and stays silent otherwise. It gives no clue about which pan is heavier.
In the normal version of this puzzle, two weighings find the heavy coin among eight.
With this broken balance, what is the minimum number of weighings that guarantees you find the heavy coin? Describe the procedure.
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The scale now gives only two answers per weighing instead of three. Recount how many possibilities each number of weighings can distinguish. Then note that an unequal result with equal numbers of coins per pan still tells you something useful.
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