Brainteaser: You have twelve coins, and one of them is counterfeit. The counterfeit coin is either heavier or lighter than the rest. You have a balance scale and can use it three times. How can you find the counterfeit coin and determine whether it is heavier or lighter?
Answer:
Divide the 12 coins into three groups of four. Weigh two of the groups against each other:
- If they balance, the counterfeit coin is in the group not weighed.
- If they don’t balance, the counterfeit coin is in the heavier or lighter group.
Take the group with the counterfeit coin and divide it into three groups of two and one single coin:
- Weigh two of the groups of two against each other.
- If they balance, the counterfeit coin is the single coin.
- If they don’t balance, the counterfeit coin is in the heavier or lighter group.
Use the final weigh to compare two of the coins:
- If they balance, the counterfeit coin is the remaining one.
- If they don’t balance, you’ll know if it’s heavier or lighter based on the previous results.