Seven SportsmenLogic puzzles require you to think. You will have to be logical in your reasoning.
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?
HintFigure out what the numbers are, and then eliminate the impossibilities.
AnswerLet 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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