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Get one half by squaring (Posted on 2004-09-20) Difficulty: 4 of 5
Can you solve the following equation?

= 1/x + 1/y +...+ 1/z

All variables must be different, positive integers, and there must be a finite number of terms.

See The Solution Submitted by Federico Kereki    
Rating: 4.2500 (12 votes)

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9 terms (or beating dead horse) | Comment 25 of 31 |
A 9 term solution would be
2, 3, 4, 5, 7, 8, 56, 168, 840

Kind of a pain, but after picking first 6 numbers, you know what the smallest possible value for the next would be (in my case it was 54). Make an Exel grid with 54-300 on the top (300 is just a big number) and 55-300 along the left.

Given the 7th (top) and 8th (left) numbers, you calculate the 9th (bc + ac + bc = abcx =>
c = ab/(abx-a-b) where x is whats left of the .5 after the first 6 variables and a,b,c are the squares of the 7th, 8th, and 9th).

Filling the grid in with the proper equation (sum-1/a^2-1/b^2-1/c^2 and conditional formatting (for 0) turns up the answer.

Rajal

(p.s. after all this work I sure hope the answer is right! Any independent verification?)
  Posted by Rajal on 2004-09-22 19:21:04
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