Given 27 table tennis balls, one is heavier than the others.
What is the minimum number of weighings (using a two-pan balance scale) needed to guarantee identifying the heavy one? The other 26 balls weigh the same.
Answer
A minimum of 3 weighings is required.
Divide the 27 balls into 3 groups of 9 balls each. Use the scale to weigh 2 groups. This will tell us which group has the heavier ball.
Now, divide the 9 balls into 3 groups of 3 balls each and weigh 2 groups, and identify the group which has the heavier ball.
From the heavier group, weigh 2 balls to determine the heavier ball.