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Ben, Fang and Venetia are playing a game in which a card numbered 2 3 4 5 6 7 or 8 is stuck to each of their foreheads, so that each player can see the other two numbers but not their own. Joey walks in and observes that the three numbers are not all different, and that the product of the three numbers is a perfect square. How many of the three players can now deduce the numbers on their foreheads?

 Dec 27, 2022
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Only one player can deduce their number.

 Dec 27, 2022

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