ou have 8 identical balls and one that is slightly heavier. Using a balance scale, what's the minimum number of times you need to weigh to find the heavier ball?

Question

2
3
1
4

Answer 1

To determine the heavier ball among 9 balls (8 identical and 1 heavier) using a balance scale, you can find it in a minimum of 2 weighings. Here’s how you can do it:

1. First Weighing: Divide the 9 balls into 3 groups of 3 balls each. Weigh two of the groups against each other.

   • If one group is heavier, then the heavier ball is in that group.
   • If they balance, then the heavier ball is in the group that was not weighed.

2. Second Weighing: Take the 3 balls from the group identified as containing the heavier ball and weigh any two of them against each other.

   • If one of those is heavier, you’ve found the heavier ball.
   • If they balance, then the heavier ball is the one that was not weighed.

Thus, the minimum number of weighings required to find the heavier ball is 2.