Can you solve this math puzzle?
You have 12 balls that look identical. However one ball is heavier or lighter than the others.
You have a balance scale and can use it three times.
How can you find the odd ball and determine whether it is heavier or lighter?
Think you know the answer?
To see the answer to the math puzzle, click to expand the accordion below.
Label the balls 1 to 12.
First Weighing
- Weigh balls 1, 2, 3, and 4 against 5, 6, 7, and 8.
- If the two sets of balls are balanced, the odd ball is among 9, 10, 11, or 12.
- If the two sets of balls are not balanced, then the odd ball is among 1 – 8.
Second Weighing
- If the first weighing was balanced: Weigh 9, 10, and 11 against 1, 2, and 3.
- If the two sets of balls are balanced, then the odd ball is 12.
- If the two sets of balls are not balanced, then you know 9, 10, or 11 is the odd ball.
- If the first weighing was not balanced: Weigh 1, 2, and 5 against 3, 6, and 9.
- If the two sets of balls are balanced, then 4, 7, or 8 is the odd one.
- If the two sets of balls are not balanced, then you know which side is heavier/light with the odd ball.
Third Weighing
- From the second weighing, compare two balls from the identified group to determine the odd one and if it’s lighter or heavier.
Need a hint?
If you need a hint, click to expand the accordion below.
Weigh multiple sets of balls at the same time so you can narrow down the odd ball to at first groups of 4 balls and then to smaller groups in the second and third weighings.
