# Plainim: the plainest of Nims

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

- On a single move, one may only add/remove chips in a single row.
- At most one chip is allowed per square.
- One may only add chips to the right of a chip being removed on the same move.
- 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 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

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

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