12 Marbles Problem

You have twelve marbles that are identical in size, shape, and color. One of the marbles is heavier in weight than the rest. How can you find the heavier marble by using a balance scale only thrice?


Split the marbles into 3 groups with 4 marbles each. Pick 2 groups and use the scale to determine which group contains the heavier marble. If the 2 groups weigh the same, the heavier marble is in the 3rd group.

Once the group is determined, split the marbles into 2 groups with 2 marbles each. Use the scale to determine the group that contains the heavier marble.

Lastly, use the scale to weigh the 2 remaining marbles to determine the heavier marble.