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 One equation with nine unknowns! (Posted on 2006-12-13)

Solve the given equation by using the integers from 1 to 9 inclusive exactly once each.

a/(b*c)+d/(e*f)+g/(h*i)=1

Note: Obviously this problem is easily susceptible to a brute force approach - however, it would be nice to see some arguments that don't use computer programs!

 No Solution Yet Submitted by John Reid Rating: 4.2000 (5 votes)

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 Solution | Comment 4 of 7 |

5/(8*9)+7/(2*4)+1/(3*6)=1

Assuming a=5 and d=7 from the first comment, I tried to rule out e,f combinations.  I found that 1,8 and 1,9 created a fraction that was too large.  Since 1*8 = 2*4, I tried to rule out 2,4 as a possibility for e,f.  In doing so, I stumbled upon the answer.

So, it wasn't brute force, but more like guess-and-check.

 Posted by Guest on 2006-12-14 14:36:03

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