Three Heavy and Three Light Balls
Three out of six lookalike balls are heavy. The other three are light. How many weighings on a beam balance are necessary to identify the heavy balls?
Three weighings suffice. There are two different techniques for solving the problem. Let the balls be numbered 1 thru 6.
- Weigh (1,2) vs (4,5), then (2,3) vs (5,6), then (3,1) vs (6,4).
- All weighings involve one ball on each side of the beam balance. First weigh 1 against 2. If these are equal, then weigh 1 against 3, otherwise weigh 3 against 4. The reader may work out what the third weighing should be.
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12 Sep 2008
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