I spent a frustrating hour trying to solve the “Gordian’s Knot” puzzle, recently given to me by a friend. The principle of the puzzle is nice: six solid polyomino pieces, formed by making holes inside 1x5x7 rectangular slabs, arranged as pairs in three orthogonal planes and initially forming a very compact “nucleus”: http://www.amazon.com/Think-Fun-6820-ThinkFun-Gordians/dp/B000EGI4OO The goal is to completely remove one of the pieces. But it’s not a fun puzzle to solve because the pieces often jam and don’t slide very freely. It wasn’t too hard to write a short computer program that random-walks its way to the solution (at each step it picks at random one of the few legal moves). I’m sharing this with math-fun because it turns out to be a nice metaphor of radioactive decay. After a period of diffusive motion where all six pieces are “bound” together, an “alpha particle” is ejected, seemingly at a random moment. Unlike the Coulomb barrier that a real alpha particle has to tunnel through, the orange piece in this puzzle has to find its way through an entropic bottleneck. From the few decays I’ve observed up to now, I estimate the half-life to be several hundred moves. **************************************************************************************** Warning: exercise extreme caution when clicking the following link: https://www.dropbox.com/s/bxcc7h2am1e49ww/alphadecay.gif?dl=0 **************************************************************************************** -Veit