A logic problem by Cosmic Curiosity
You have eight seemingly identical steel balls and a two arm balance scale. One of the balls is slightly heavier than the others, but you can’t tell which one by just looking at all the balls. Using the scale, what is the least number of times you will need to do a weighing to find out which ball is the heavy one?
The answer is 2.
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1 solution
1) Weigh 3 vs. 3. Either the scale will balance or the scale will not balance and one side will be heavier.
2a) If the scale is balanced, then the heavy ball can’t be one of the balls that was weighed, so it has to be one of the remaining 2 balls. Weigh 1 vs. 1 for the remaining 2 balls. The one that is on the heavier side is the heavy ball.
2b) If the scale was not balanced, then the heavy ball has to have been one of the balls that was weighed, and has to be one of the three balls on the heavier side. Weigh 1 vs. 1 of the 3 balls. If the scale balances, then the ball that didn’t get weighed is the heavy ball. If the scale does not balance, the ball on the heavier side is the heavy ball.