Puzzle: You have 12 coins, one of which is counterfeit, and a balance scale. The counterfeit coin is either heavier or lighter than the others. How can you identify the counterfeit coin and determine whether it is heavier or lighter in just three weighings?
Answer:
- Divide the coins into three groups of four. Weigh two groups.
- If they balance, the counterfeit coin is in the third group.
- If they don’t, the heavier or lighter side contains the counterfeit.
- Take the group with the counterfeit and divide it into three coins, weighing two.
- If they balance, the third is counterfeit.
- If they don’t, you know whether it’s heavier or lighter.
- With the remaining three coins, weigh two to find the counterfeit.