Play · Hard
Twelve coins
Twelve coins. One is fake, and it's either heavier or lighter. You don't know which. Three weighings to find the fake and say whether it's heavy or light.
The puzzle
How to think about it
Count the outcomes
Count first: 12 coins × heavy or light is 24 possibilities, and three weighings give 3 × 3 × 3 = 27 outcomes. It only just fits, so every weighing has to split what's left into three even parts. Start with 4 against 4. If it tips, coins on the heavy side can only be heavy and coins on the light side can only be light. Mix them on the second weighing: try 1, 2 and 5 against 3, 4 and 6.