You have 12 identical-looking coins, one of which is counterfeit and weighs slightly different (either lighter or heavier) than the other 11. On your first weighing using a balance scale, you place 4 coins on the left pan and 4 coins on the right pan, and the scale balances perfectly. What should your second weighing be to guarantee finding the fake coin in 3 total weighings?
Weigh 3 of the remaining 4 unweighed coins against 3 known genuine coins.
Since the first 8 coins balanced, all 8 are genuine and the fake is among the remaining 4 unweighed coins. Weighing 3 unweighed coins against 3 genuine coins will either tilt (showing the fake is among those 3 and whether it is heavy/light) or balance (showing the 4th unweighed coin is fake). This guarantees isolating the fake coin on the 3rd weighing.
About this riddle
Logic riddles give you a few facts and ask what must be true. List what you know, cross out what cannot be, and see what is left.
Difficulty: Hard. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
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