Puzzle – Find Odd Stone

You are given a digital scale and 12 identical-looking Stones, out of which one is heavier than the rest ( you don’t know which ). You are only allowed to use the scale three times to identify the odd stone and determine whether it is heavier than the rest. How can you do this?

Find the odd stone heavier than others

Solution:

• Divide the stones into three groups of four.
  Weigh two of the groups against each other. If they balance, the odd stone is in the third group; if one is heavier, the odd stone is in that group; if one is lighter, the odd stone is in the other group.

Matching groups of 4

• Take the group with the odd stone and weigh two of the stones against each other. Which group is heavier next check in that? If one is heavier, that is the odd stone; if one is lighter, the odd stone is the other stone.

Matching groups of 2, and then 1 to find out.

This solution works because you are able to eliminate two-thirds of the stones with each weighing, ultimately finding the odd stone with just three weighings.