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Puzzle - Hint

You have 12 coins, one of which is fake. The fake coin is indistinguishable from the rest except that it is either heavier or lighter, but you don't know which. Can you determine which is the fake coin and whether it is lighter or heavier using a balance scale and only 3 weighings?

Puzzle Image

 [Ref: ZLKY]

Hint: Finding the correct weighings requires some very careful thinking.

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