Ben, Fang, and Venetia are playing a game in which a cardnumbered 2, 3, 4, 5, 6,

Question

Ben, Fang, and Venetia are playing a game in which a cardnumbered 2, 3, 4, 5, 6, 7, or 8 is stuck to each of theirforeheads, so that each player can see the other two numbers butnot their own. Joey walks in and observes that the three numbersare not all different, and that the product of the three numbers isa perfect square. How mnay of the three players can now deduce thenumbers on their foreheads? Please use full explanation. Ben, Fang, and Venetia are playing a game in which a cardnumbered 2, 3, 4, 5, 6, 7, or 8 is stuck to each of theirforeheads, so that each player can see the other two numbers butnot their own. Joey walks in and observes that the three numbersare not all different, and that the product of the three numbers isa perfect square. How mnay of the three players can now deduce thenumbers on their foreheads? Please use full explanation.

Explanation / Answer

given that not all the three numbers are different. from this , we can follow that all the three numbers are sameor atleast two of the three are same. but , if all the three are same , then the possibilityis 4,4,4 whose product is 82. the other possibility is two are same and thethird is different. they can be 5 , 5 , 4 whose product is 102 or, 6,6,4 whose product is 12 2

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