No, Fred, it wasn't Chomp; it was more similar to this game. By the way, how about if we first try to solve the game obtained by ignoring the rule about always making a move that grabs the maximum possible number of cubes. (We could call that one "Getting Cubes".) And ask what is the minimum number of moves to Get all cubes. Is it possible that in the 5 x 13 x 31 case (and for any K x L x M box with K, L, M pairwise relatively prime and K < L < M), then the subset of the box having the (mod K, mod L, mod M) coordinates given by {(j, j, j), 0 <= j < KL} must require at least KL turns to remove? Showing that whichever of the two games are being played, KL is a minimum number of moves for removing all cubes? —Dan
On Mar 11, 2016, at 5:10 PM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
On 3/11/16, Dan Asimov <asimov@msri.org> wrote:
... But somehow I feel as if I've seen a game like this before somewhere; I just don't recall where.
—Dan
You're not thinking of Conway's "Chomp" game, by any chance? WFL