Thane>People might be interested in some correspondence between Martin Gardner and
David Klarner (ca 1987) on related packing problems that I have on this page
http://www.plambeck.org/oldhtml/mathematics/klarner/martingardner/index.htm
Cool. Wasn't Klarner arrested for his habit of clandestinely refurbishing cannon in public parks and then firing them in the middle of the night? In the house where I live is a redwood 5x5x5 that Klarner made for Richard Weyhrauch. I still don't understand why there's a 2x2x2 in Conway's 5x5x5. Is there a nice proof that it always needs to contact the 2x2x1? But its ability to do so in a 1x2 area makes it replaceable by another 4x2x1. --rwg PS, A program I wrote finds several solutions/sec to the 7x7x7, e.g. www.tweedledum.com/rwg/7x7x7sol.gif , but only if told where the odd pieces go. When I permute them to be no longer cornerwise connected, yet consistent with the 21 parity constraints, it finds no solutions after many minutes. I assume the same holds for the 5x5x5 (15 constraints), which is probably small enough to search exhaustively. In the 7x7x7, replacing two 2x4x1s with a 15th 4x4x1 had no luck running overnight.