Find the heavy ball
You have 9 identical-looking balls. One is slightly heavier than the rest. Using a balance scale, what is the fewest weighings that always finds the heavy ball? How?
Show hint
A balance has three outcomes, not two: left heavier, right heavier, or level.
Show solution
2 weighings.
- Weigh 3 balls against 3. If one side is heavier, the ball is in that group. If they balance, it is in the 3 you left out.
- From that group of 3, weigh 1 against 1. The heavier side is the answer; if level, it is the third ball.
Each weighing divides the options by 3, so k weighings handle up to 3k balls.
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