Chomp

Alternate Names

Subtract-a-Square and Take-a-Square are names of variants of this game.

No. of Players

Two

Equipment

Fourteen counters of one color and one of another color are required for play. They are arranged in a 3x5 rectangular “chocolate bar” with the distinguished counter at the top left.

History

The idea of playing this game with a chocolate-bar analogy is credited to the American mathematician David Gale, but similar recreational mathematical concepts under different names appear in earlier literature.

Objective

A player who is forced to make the last move and eat the poisoned counter loses the game. Thus, his opponent is the winner.

Play

The two players take alternate turns choosing one counter and "eating it" by removing it from the board. Also removed are any counters which are below and to the right of the chosen counter. The top left block is "poisoned" and the player who eats this loses the game. A game is shown below:

Opening position

First player removes six counters.

Second player removes two counters.

First player removes four counters.

Second player removes remaining counters and wins by forcing first player to eat the poisoned counter.

Strategy

Variations

Like the related game of Nim, Chomp lends itself very well to numerous variations and related mathematical exercises. Any combination of the following variations of the rules could probably be used.

  • The size of the "chocolate bar" could be just about any size, or any number of counters arranged in rows and columns.

  • In the rules described above, the player may only remove a square or rectangle from the bottom right edge of the bar. Alternative rules could allow a player to remove a rectangular section of any size from any edge of the bar. Also a player could be prohibited from removing counters in perfect squares of one single counter, four counters in 2x2 formation, nine counters in 3x3 formation and so forth.

  • The "poison" part of the chocolate bar need not be at the top left and may be any location on the board.

  • The rules above say that a player who is forced to eat the last section of the chocolate bar is the loser, this means that the game is a misère game. Alternatively, the game could be played as a normal play game, meaning that the player who is able to eat the specially marked counter (obviously no longer considered poisonous) is the winner.

Sources