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An alternating grid-removal game in which choosing an occupied cell removes it and every occupied cell above and to its right. The player who removes the designated lower-left poison cell loses. Reachable occupied-cell sets are order ideals for coordinatewise order. A nonempty reachable position always contains the poison cell, and removing that cell empties the board. The monotone boundary representation of a grid order ideal supports compact board updates.

For Chomp, one representation is a Boolean array occupied(y)(x) with one entry per cell. The initial board has every entry true. For the noninitial board in the figure, the sets of occupied column indices in successive rows $y=0,1,\dots ,5$ are $\{0,1,2,3,4,5\}$, $\{0,1,2,3\}$, $\{0,1,2,3\}$, $\{0,1\}$, $\varnothing$, $\varnothing$; all other entries are false.

A more compact representation is the monotone boundary representation of a grid order ideal: an array row(y) giving the number of occupied cells in row $y$. Occupied cells in a row always form a left prefix. The initial representation is $[6,6,6,6,6,6]$, and the illustrated noninitial representation is $[6,4,4,2,0,0]$, indexed upwards from row zero. Its total is $16$. These descriptions use the same coordinate orientation as the original figure; no source image is needed in the solution.