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".

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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 http://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.

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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.

Reference

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

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