Rich Mann

04-28-2006, 08:43 PM

I am thinking about an art project that, in part, consists of a large square divided into smaller square areas. It occurred to me that it would be more elegant (in the sense of an elegant solution or proof) if every sub-square was a different size--and more elegant still if the subsquares were inclusive starting with one.

I began adding up the squares of the whole numbers, in order, and found that the cumulative sum of the first 24 squares added to 4900 (70 squared). I don't know if this, necessarily, means that those 24 smaller squares can be jigsawed into a 70x70 area, or not. It seemed to me, though, that this is the kind of thing that someone might have figured out before.

So, before I cut out a bunch of little squares of paper and start fiddling with them or try to write a complicated, brute-force program, I thought I might as well ask the smartest and most knowledgeable people that I know about it.

So, do any 'Dopers out there know if there is a solution to this puzzle and can point me to it?

I began adding up the squares of the whole numbers, in order, and found that the cumulative sum of the first 24 squares added to 4900 (70 squared). I don't know if this, necessarily, means that those 24 smaller squares can be jigsawed into a 70x70 area, or not. It seemed to me, though, that this is the kind of thing that someone might have figured out before.

So, before I cut out a bunch of little squares of paper and start fiddling with them or try to write a complicated, brute-force program, I thought I might as well ask the smartest and most knowledgeable people that I know about it.

So, do any 'Dopers out there know if there is a solution to this puzzle and can point me to it?