# The Game Discrete

Inspired by my post about tic-tac-toe I want to introduce a game. It is played on a 3x3x3 grid or equivalently on a 9×3 grid:

Originally I thought that this would be a two-player game, but there is no reason why this couldn’t be an n-player game for any n. The players make moves one after another. A move consists of drawing either a cross or a circle in one of the free squares in the grid. Each player may choose to draw either a cross or a circle. Suppose a player makes a discrete line (see later) consisting only of crosses or only of circles on his or her move. Then, if the next player notices it, he or she should say (or shout!) "discrete". In that case the previous player, the one who made the line, drops from the game. Then other players continue. If someone says "discrete" but the previous player didn't make a line, then the shouter drops. There is no other way to drop. If, say, someone introduces a line but it is not noticed immidiately, it doesn't count.

The winner is the one who does not drop out. Everybody else are losers :-P

What I mean by a discrete line is explained in the entry about tic-tac-toe, but is also explained visually in this pdf-file.

Notes:
1. As was mentioned in the entry about tic-tac-toe, the cube cannot be coloured with two colours without introducing a monochromatic discrete line. This implies, that one of the players must be creating a line at some point.
2. If all players are perfect players (i.e. they do not make unnecessary lines, they notice always their predecessor’s lines and never make mistaken claims), then the initial position (number of players, who moves first, what is the order of the players) determines the winner.
3. If you want more randomness, you can randomize the next player at each move; so that players do not move in a prescribed order.
4. One can extend this to 3x3x3x3 or to 4x4x4 and introduce more colours.
5. To make the game longer and maybe more interesting: whenever a player drops by introducing a line, erase that line before continuing.
6. Instead of dropping a player give him or her just a negative point.
7. If you tried to play, it would be nice to know whether it was fun.

## About Vadim Kulikov

For details see this
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