Plainim: the plainest of Nims

Plainim is played on a checkered board by removing or adding chips. There are just a few rules.

  1. On a single move, one may only add/remove chips in a single row.
  2. At most one chip is allowed per square.
  3. One may only add chips to the right of a chip being removed on the same move.
  4. The one to remove the last chip wins.

To perform a move click on squares (in a single row) where you want chips placed or removed (see that you confirm to Rules 1-3). Then press the button "Make Move".

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at, download and install Java VM and enjoy the applet.

This is the latest among various incarnations of Nim. Each column represents a binary digit. Each row represents a heap. This variant is the simplest in that you are explicitly given a binary presentation of numbers. All that's needed is to see that after your move only matched digits are left over. This variant is on a preschooler level.

Plainim misère, is only a little different: the player who removes the last chip loses the game.


  1. R. K. Guy, Fair Game, Comap's Explorations in Mathematics, 1989

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