hi Bill, what are the radii of the 12? W. -----Original Message----- From: R. William Gosper [mailto:rwg@spnet.com] Sent: maandag 11 augustus 2003 22:12 To: math-fun@mailman.xmission.com Subject: [math-fun] surprisingly hard knapsack puzzle Last month I had the pleasure to visit the Microsoft Theory Group. Mike Sinclair and Gary Starkweather in a neighboring group generously helped me laser-cut a puzzle consisting of an 8" circular tray and twelve unequal circular disks ranging from .86" to 2.8". To my amazement, *no one* has yet succeeded in fitting all twelve disks back into the tray, although Christian Borgs, a Microsoft physicist, solved two slightly easier versions, one of which, unfortunately, gave him the answer to the harder version. I believe the solution to the current version is unique, but my first "cut" neglected to allow for the .006" diameter of the laser beam, and this small amount of slop permitted at least three unintended solutions. The current version is fairly pleasant to see and work, and draws small crowds when worked in public. Thus it invites frequent and prolonged attacks, but protects itself with the "too many cooks" effect. This puzzle is also fairly resistant to computer solution--I'm not even sure how to quantify the combinatorics of the search. --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun =============================== This email is confidential and intended solely for the use of the individual to whom it is addressed. If you are not the intended recipient, be advised that you have received this email in error and that any use, dissemination, forwarding, printing, or copying of this email is strictly prohibited. You are explicitly requested to notify the sender of this email that the intended recipient was not reached.