Three Heavy and Three Light Balls Puzzle - Solution
The Puzzle:
How many weighings on a beam balance are necessary to identify the heavy balls?
(A Martin Gardner puzzle)
Our 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.
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.
Puzzle Author: Martin Gardner