Hmm, what about other rectangles also with area pi^2/6 ? For example the pi/sqrt(6) x pi/sqrt(6) square. Is there any one of these where such a packing is known to be possible or known to be impossible? And I have to add, of course: What about the potentially easier question of packing the 1/n x 1/n squares into a flat *torus* of area pi^2/6 ? (For that matter, what about other open sets of area pi^2/6 ? Conjecture: Given an open set O that for each n >=1 can contain disjoint open squares of sides 1, 1/2, 1/3,...,1/n , then O can contain disjoint squares of all sides 1/n, n >= 1 simultaneously. --Dan --------------------------------------------------------------------- Jim Propp writes: << Since the sum of the reciprocals of the squares of the positive integers is pi^2/6, the question arises as to whether squares with sides 1, 1/2, 1/3, etc can be packed into a rectangle of size 1 by pi^2/6. A picture of such a packing appears at http://www.pisquaredoversix.force9.co.uk/Tiling.htm I know of no proof that such a packing is possible or impossible. A program which I wrote has recently packed the first one million such squares into such a rectangle. . . .

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