Seven Sportsmen
Logic 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 1digit 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.
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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 1digit 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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Comments
WildCardAl
Oct 08, 2007
 Silly me !!! I messed up the onedigit clue and used 1 thru 7 and tried to solve but couldn't !!!
Good one !! 
scallio
Oct 10, 2007
 You lost me with your answer, but I got the correct answer writing it out and had fun doing it!
4  3  8  2  5  1  9

shenqiang
Oct 10, 2007
 Scallio, you're wrong. I said the PRODUCT, not the SUM. 
IQ_master
Oct 13, 2007
 confusing but fun!!! 
onua9159
Oct 19, 2007
 Good teaser! It was extremely fun 
seventy7
Dec 18, 2007
 hmmmm...i'm lost. i guess it's just not my thing. interesting, though. 
opqpop
Jan 30, 2010
 Pretty nice solution. I actually solved it pretty quick just by guessing.
You need to satisfy ab = de and cd = fg. I tried d = 0 and 1 and quickly saw those don't work. When I got to d = 2, I saw 3 * 6 = 2 * 9 and 2 * 4 = 1 * 8. 
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