Can you solve the following equation?
½ = 1/x² + 1/y² +...+ 1/z²
All variables must be different, positive integers, and there must be a finite number of terms.
In answer to David Shin's question, my method was to take out a spreadsheet and let excel calculate the sum and what next variable (integer or not) could finish the job. I just played around with different variables to see what would work, and my infinite solution seemed to converge on .5. e.g. seems to have used a similar method, but he obviously did a lot better than I did, because he got a finite solution. Great job, e.g.
I was very surprised to see that e.g. had found a finite solution, so I had a little more courage and gave the excel spreadsheet another try... this time using a 30 instead of a 25.
I found a 10 term solution within a minute, using the following terms:
2,3,4,5,6,12,30,60,75,100
Hmm, well no wonder we had trouble proving this puzzle impossible.

Posted by Tristan
on 20040921 22:04:06 