I think this game is now pretty much cooked. The Conclusion in my write-up is: Boxes are classified according to their dimensions into "tall" and "short". Tall boxes have game length equal to the product of their two smaller dimensions, which is also an upper bound on game length of all boxes. Most short boxes have several possible game lengths, but there are a few exceptions. The comparison n1 + n2 - 2 : n3 distinguishes tall (<) from short (>=) boxes. Monte Carlo analysis was used to investigate the game, and to derive and support the above test. It is possible, though unlikely, that further exception cases exist among short boxes larger than those explored. A variant called Getting Cubes has behavior similar to Grabbing Cubes, but differs in the details of exception cases and shape of the game length distributions for short boxes. The box in the original "Problem 327" published in Playground is 5 x 13 x 31. This is a tall box. Therefore, the magazine's claim that the game always lasts 65 moves, is correct. However, some discussion of why that box is not one with varying length games, might improve the published proof. http://www.mikebeeler.com/grabcube-v5.txt <http://www.mikebeeler.com/grabcube-v5.txt> Thanks everyone, — Mike