Two weighings to isolate the heavier of nine marbles
Question
You have nine marbles that look the same; one weighs more than the rest, which are identical. What is the fewest number of uses of a two-pan balance that guarantees finding it, and how?
Short answer
Two. A weighing has three outcomes, so two weighings distinguish up to cases. Put three marbles on each pan with three aside: the heavy pan, or the set-aside trio if balanced, contains it. Then compare two of those three, again keeping one aside.
Adapted from Joshi, Denson & Downes, Quant Job Interview Questions and Answers, Q8.16, p.277; question and answer rewritten by SelfMadeQuant.com.
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Open the worked solutionLessons behind this question
- Sample Spaces, Events, and the Probability Axioms
- Conditional Probability, Total Probability, and Bayes' Rule
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