The Odd Coin
One coin differs in weight. With only a few uses of a balance scale, find which coin it is and whether it is heavy or light. Start with the easy version: 9 coins, one heavy, 2 weighings.
Weighings used: 0 / 2
How to play
Tap a coin to move it from the table to the left pan, then the right pan, then back to the table. Put the same number on each side and press "Weigh": the scale tips and shows the result. You only have a fixed number of weighings. When you know, pick the coin number and press "Answer" (in the 12-coin version, also say heavy or light). "Hint" gives the idea, the number of candidates, then a concrete weighing. "Auto-solve" follows a correct decision tree and shows how the candidates shrink with each weighing.
Learn more
A balance scale has three outcomes: left side down, right side down, or level. Two weighings give 3 x 3 = 9 outcomes in total, and three give 3 x 3 x 3 = 27. With 12 coins, each possibly heavy or light, there are 12 x 2 = 24 possibilities. Since 24 is more than 9, two weighings can never be enough, however clever you are. Since 27 is at least 24, three weighings might work, and a real strategy exists. But having enough outcomes is not the same as having a plan: weighing 6 against 6 first leaves 12 possibilities, which two more weighings (at most 9) cannot separate. The right first step is 4 against 4. This page builds the decision tree by exhaustive search, and tests that it identifies all 24 cases within three weighings and that no 2-weighing strategy exists.