Answer: If you have 10 balls and one of them is defective (either heavier or lighter), you can find the defective ball in a maximum of 3 weighings using a two-pan balance scale.
Here’s how you can do it:
Divide the balls into three groups of three balls each and one group with the remaining ball.
Weigh two groups of three balls against each other. If they balance, the defective ball must be in the third group of three balls or the group with the remaining ball. If they don’t balance, the defective ball must be in one of the two groups being weighed.
Take two balls from the group that contains the defective ball and weigh them against each other. If they balance, the defective ball must be the remaining ball in that group. If they don’t balance, you have found the defective ball.
This method guarantees that you will find the defective ball in a maximum of 3 weighings.