On 10/03/2016 17:11, James Propp wrote:
Am I the only one who is dissatisfied with the solution to Problem 327 in the Playground feature of the February 2016 issue of "Math Horizons" (see http://digital.ipcprintservices.com/article/The_Playground/2387298/289441/ar... , page 31)?
To show that a certain cube-grabbing game always ends in 65 moves, the authors first show that an obvious way to play the game ends in 65 moves, and then show that "the algorithm for removing the maximum number of cubes at each steps takes 65 steps".
But I don't see why it follows that EVERY way to play the game ends in 65 moves.
The problem statement says | Assume that each player takes as many cubes as possible each turn. However, I haven't thought about the question enough to be sure of whether there are nontrivial differences between different ways of playing that break ties (among choices that take as many cubes as possible each turn) in different ways. -- g