Math Game Monday: Wythoff’s Nim

“Wythoff’s Nim” is free on this website for one week only. It’s an excerpt from 312 Things To Do with a Math Journal, available as an ebook at my bookstore (Thank you for cutting out the middleman!) and in ebook or paperback through many online retailers. Read more about my playful math books here.

Many parents remember struggling to learn math. We hope to provide a better experience for our children.

And one of the best ways for children to enjoy learning is through hands-on play.

Use this strategy game to prompt math writing: What did your children notice about the game? How did they decide their moves? How is this a Nim game?

Wythoff’s Nim

Math Concepts: chess moves, strategic thinking.

Players: only two.

Equipment: chess set or graph paper.

How to Play

With a chess set, place the black king on the lower-left corner square. If using graph paper, draw a star in the lower-left corner square.

The first player places the white queen (if using graph paper, draw an X or crown shape) on any square in the top row or farthest-right column.

In succeeding turns, each player moves the queen any number of squares in a straight line to the left, down the board, or diagonally. On graph paper, the player makes a mark at her new position.

The queen moves always in the direction of the star, never away from it.

The player who moves into the final square, capturing the star, wins the game.

A chess queen can move any number of spaces in a straight line, but she cannot jump over another piece. When the queen moves into a square with an opposing piece, she captures that piece.

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