While 1^2 + ... + 24^2 = 70^2 cannot be packed into a square of size 70, 2 (1^2 + ... + 24^2) = 70x140 can be packed, Gunter Sterten found this; http://www.squaring.net/140x70-2x24squares.png. He said it was at the edge of what could be packed with his program 4(1^2 + ... + 24^2) = 140^2 can also be packed, Eric Friedman found this; http://www.squaring.net/140x140-4x24squares.jpg by hand Stuart Anderson

On Fri, Jun 3, 2011 at 8:49 AM, Dan Asimov <dasimov@earthlink.net> wrote:

...

((( My favorite number is 24 hands down, because of its amazing properties like showing up in Dedekind eta, 1^2 + ... + 24^2 = 70^2 being the only such relation, the 24-dimensional Leech lattice, and 24 being the largest number N such that all smaller numbers K with GCD(K,N) = 1 satisfy K^2 == 1 (mod N). At least some of these are interconnected. )))