General
The 12 Coins Puzzle: Find the Fake with One Balance Scale
You have 12 identical-looking coins; one has a different weight (heavier or lighter). Using a balance scale (no weights), what is the minimum number of weighings needed to identify the odd coin AND determine whether it is heavier or lighter?
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What is the answer to the 12 coins balance scale riddle?
3 weighings. With a two-pan balance you can sort 27 outcomes in three weighings, which covers all 24 possible cases (12 coins x 2 states).
Why is 3 the minimum and not 2?
Each weighing has 3 outcomes (left heavy, right heavy, balanced). Two weighings give only 9 outcomes, too few for 24 cases. Three give 27, which is enough.
Do you find the fake coin and whether it is heavier or lighter?
Yes. A careful 3-weighing strategy identifies the odd coin and reveals if it is heavier or lighter than the rest.