Kayles
This game is taken from the book On Numbers and Games by John Conway (Academic Press, 1976). The game was originally proposed by Dudney. When it is combined with ideas from the game of Rim, then you have the game of Rayles.
What you need
- Any number of coins, poker chips, toothpicks, scraps of paper, etc. that can be used as markers.
How to play
- Set up the game by arranging the markers in groups with gaps. A "group" is some number of markers that are touching one another. Any number of markers can be in these groups -- ridiculously many, or just one. A gap is the space between groups.
- Here is a sample set-up:
- Players take turns removing coins as follows:
- On one turn, a player may remove either 1 marker, or two markers that are touching each other.
- Notice that you can remove markers in such a way as to divide a single group into two groups.
- The player who picks up the last marker loses.
- Here are some moves that can be made in the game that was set up above. Which player do you think will win?