Suppose you had eight apparently identical billiard balls, but one of the eight is slightly heavier than the others. The only tool you have to measure is a balance scale. What’s the fewest number of times you’d have to use the scale to find the heavier ball?
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You can determine exactly which ball is heavier by using the scale only twice. The key to the puzzle is not only getting information by what you measure but also gaining information but what you do not measure.
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Separate the 8 balls into 3 piles: two piles of 3 balls and one pile of 2 balls.
Use the scale to compare the two piles of 3 balls. If the heavier ball is in one of the piles of three, then you can use the scale to compare two of the three. You will either have the heavier ball or the ball not measured is the heavier.
If the ball isn’t in one of the piles of 3 weighed, then it’s in the pile of two and you can use the scale to compare those.