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## Seven Sportsmen

Logic puzzles require you to think. You will have to be logical in your reasoning.

 Puzzle ID: #38430 Fun: (2.59) Difficulty: (2.98) Category: Logic Submitted By: shenqiang

Seven sportsmen are standing in a row. Each sportsman has a different 1-digit number. The product of the first three, the product of the middle three, and the product of the last three are all equal.

What's the middle sportsman's number?

Let their numbers be a through g, we have abc=cde=efg.

5 or 7 cannot occur, because they are prime and no other 1-digit number contains them. Therefore, the numbers are 1, 2, 3, 4, 6, 8, 9.

Since abc=efg, abcdefg/d is a perfect square. 1*2*3*4*6*8*9=2^7*3^4, and d can be only 2 or 8.

If d=2, the numbers 1, 3, 4, 6, 8, 9 can be made into 1*8*9=3*4*6=72, and we can have c=9, e=4: 9*2*4=72.

If d=8, the numbers 1, 2, 3, 4, 6, 9 can be made into 1*4*9=2*3*6=36, but 36 is not divisible by 8.

Therefore, the middle sportsman's number is 2.

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