Top Puzzle 13: The 12 Identical Balls Problem | Puzzles for Interview - Interview Preparation PDF Download

Problem Statement

There are 12 identical balls, out of which one is slightly heavier than the others. You have a balancing scale and can only use it three times. How can you determine which ball is the heaviest one?

Solution

To solve the problem, we need to divide the 12 balls into groups and weigh them against each other using the balancing scale. Here's how we can do it:
1. Divide the 12 balls into three groups of four each.
2. Weigh two of the groups against each other.
Case 1: If both groups weigh the same, the heavier ball must be in the third group which we have not weighed yet.
3. Weigh two balls from the third group against two balls from any of the other two groups.
Case 1.1: If both groups weigh the same, the heaviest ball is the remaining ball in the third group.
Case 1.2: If one of the groups is heavier, then the heaviest ball is in that group.
Case 2: If one of the groups is heavier, the heaviest ball must be in that group.
3. Take two balls from the heavier group and weigh them against each other.
Case 2.1: If they weigh the same, the heaviest ball is the remaining ball in the heavier group.
Case 2.2: If one of the balls is heavier, it is the heaviest ball.

Conclusion

In conclusion, we can determine the heaviest ball out of 12 identical balls using a balancing scale in three steps. We divide the balls into three groups, weigh two of them against each other, and then narrow down the group of potentially heavier balls with each subsequent weighing. By following this method, we can find the heaviest ball in three weighings or less.