Although a different packing allows for 1..8 to be placed in a 15x15 sqtare. Is 2n-1 a upper bound then too? While I'm here, wrt Kepler's conjecture, is it true that the densest packing obeys the rule that every continuous subset of spheres must also have the densest packing possible? Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com -----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com]On Behalf Of Jon Perry Sent: 22 October 2003 12:33 To: Maths is Fun Subject: [math-fun] Mr. Perkins Quilt This MPQ talk is similar to a problem I had considered - what is the smallest square needed to house all 1..n squares? e.g. with 1x1, we need a 1x1 square with 1x1 and 2x2, we need a 3x3 square with 1x1, 2x2 and 3x3, we need a 5x5 square. So a lower bound is 2n-1. However with all the squares from say 1 to 8, this packing fails. Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun