## Pousse

### The Game

Pousse (French for "push", pronounced "poo-ss"), is a 2-person game, played on an N-by-N board, usually 4-by-4.

The players are typically labeled X and O. The rows and columns are numbered from 1 to N, starting from the top left:

Initially, the board is empty. Player X goes first. Players take turns inserting one of their markers on the board. A marker can be inserted on the board only by sliding it onto a particular row, from the left or from the right, or onto a particular column, from the top or from the bottom. Thus, there are 4*N legal moves at each turn. They are named Li, Ri, Ti, and Bi, respectively. where i is the number of the row or column.

If a player makes a move into an occupied square, all markers on the row or column of the insertion move one square in the direction of the insertion square, up to the first empty square. Ife there are no empty squares, then the last marker in the row or column is pushed off the board.

A row or a column is a straight for one of the players if every square in it contains that player's marker.

The game ends when a move creates one of these conditions:

• More straights for one player than for the other player. The player with more straights wins.
• A board position that has been reached previously in the game. The player who made the move loses.

A game always leads to a win by one of the two players. Draws are impossible.

### Example Positions

Suppose that a game began this way:

```        X  O
1. L1 T1
2. L1 L1
```

The board go through this sequence of positions.

Here is a board position after Player O has played a winning move.

If Player X could make one more move, she could create a straight with either T2 or B2.

Eugene Wallingford ..... wallingf@cs.uni.edu ..... October 12, 2012