[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
participants (1)
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R. William Gosper