### Brain Teasers

# Seven Sportsmen

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?

What's the middle sportsman's number?

### Hint

Figure out what the numbers are, and then eliminate the impossibilities.### Answer

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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