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Wed 13 Jul, 2005 08:16 pm
There are eight baseballs, all exactly alike in size and appearance, but one is heavier than any of the other seven. (The other seven are all the same weight.) With a balance scale how can the heaviest baseball be positively determined with only two weighings?
Actually it's pretty simple. On the first weighing, you put three balls on each side. If they balance, you know that the two you didn't weigh has the heavier ball which you can determine by your second weighing. However, if one of the six balls are heavier, you can weigh the two from the heavy side. If they balance, you know that the ball you left out is the heavy one. Otherwise, one of the two will be heavier.
There can be up to 9 balls:
Number them 1-9
Weigh 123 vs. 456
Outcome: Conclusion
123 is heavier: The heavy ball is 1, 2, or 3
456 is heavier: The heavy ball is 4, 5, or 6
123 = 456: The heavy ball is 7, 8, or 9
Call the heavy set (from above) A, B, and C
Weigh A vs. B
Use the same logic as above to determine which ball is heavy.
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