12 coins Puzzle
You have 12 coins and a 2-pan balance scale. One of the coins is counterfeit. the counterfeit coin is either slightly heavier or slightly lighter than all the others. Can you find the counterfeit coin in three weighings? Any change of coins on either side of the scale is considered to be a weighing.
12 Coins - Solution
Number each coin from 1 to 12. Weigh 1, 2, 3, 4 against 5, 6, 7, 8. either 1 side is heavier or they balance. If they balance, go to part 2.
- If 1 side is heavier (suppose it is 1, 2, 3, 4 ), weigh 1, 2, 3,
5 against 4, 9, 10, 11.
- If 1, 2, 3, 5 is heavier, then 1, 2 or 3 is counterfeit and heavy. Weigh 1 against 2 to find the counterfeit heavy coin, if they balance, 3 is counterfeit and heavy.
- If 4, 9, 10, 11 is heavier, then: either 4 is heavy or 5 is light. Weigh 4 against 9. If they balance, 5 is counterfeit and light - otherwise, 4 is counterfeit and heavy.
- If they balance, then 6, 7, or 8 is counterfeit and light. Weigh 6 against 7 to find the counterfeit light coin, if they balance, 8 is counterfeit and light.
- Weigh 9, 10, 11 against 1, 2, 3.
- If they balance, 12 is counterfeit. Weigh 12 against any other coin to determine if 12 is heavy or light.
- If 9, 10, 11 is heavier, then 9, 10 or 11 is counterfeit and heavy. Weigh 9 against 10 to find the counterfeit heavy coin, if they balance, 11 is counterfeit and heavy.
- If 9, 10, 11 is lighter, the above situation applies in reverse.