Three Heavy and Three Light Balls
12 Sep 2008
Puzzle

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?

Source

Mathematical Circus (1979, 272 pages) by Martin Gardner.

Solution

Three weighings suffice. There are two different techniques for solving the problem. Let the balls be numbered 1 thru 6.

  1. Weigh (1,2) vs (4,5), then (2,3) vs (5,6), then (3,1) vs (6,4).
  2. 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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