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## Three Sportsmen

 Category: Logic Submitted By: shenqiang Fun: (2.36) Difficulty: (2.75)

Three sportsmen, Tom, Jim and Sam, are standing in a row, and we can see their backs. Each of them wears a suit, which are red, yellow and blue in no particular order. Each suit has a different number, between 2 and 9, inclusive. Clues are:

1. In the order they stand, the three numbers form a perfect square.
2. Tom's number is smaller than the rightmost sportsman's number.
3. The yellow suit's number is odd.
4. The factorial of Sam's number, plus one, is divisible by the red suit's number.

Left: Tom, yellow, 5;
Middle: Jim, red, 7;
Right: Sam, blue, 6.

From clue 4, the red suit's number must be greater than Sam's number, and must be odd. By trial and error, the possible combinations are (3,2), (5,4), (7,3), (7,6).
From clue 1, the square can only be 324 or 576, where 3 or 7 is the red suit's number.
From clue 3, the square must be 576, and 5 is the yellow suit's number and 6 the blue one.
From clue 2, Tom must be the 5 and Jim the 7.