Quote by ramsey2879
I think your coding problem would be simpler if you programmed it to always choose the the smallest possible element first, i.e. first look at 1,1,1,x^2 if there isn't an x^2 then look at 1,1,4,x^2 then if there isn't an x^2 increment the 4 up to a 9 or 16, when you run out of increments of the third element, i.e. no x^2 for 1,1,16 then try incrementint the 2nd and third element to a 4, i.e. 1,4,4,x^2. when you find that there is no x^2 you would natually increment the third element to a 9 and find a solution. This method would work every time.
Sorry I meant to Quote the OP's last post.

That would be a good way for finding sums of n numbers that sum to number of a given power, but it wouldn't work the other way around: finding n for a given power.