L-game
History
L-game's humble beginnings started during a dinner conversation between Edward de Bono and mathematician Professor Littlewood. Both agreed that chess was difficult because of its complexity and many pieces. De Bono, who loves to play games but hates to focus on many pieces, took up the challenge to create a game that required skill, yet was also fun and simple to play. The result was L-game. There are 2,296 unique positions under symmetry (18,268 if redundant positions under symmetry are counted).
The Board
L-game is played on a four-row, four-column grid.
The Pieces
There are four pieces — a blue L-piece, a red L-piece, and two 1-by-1 neutral pieces. Each L-piece covers four cells of the grid at any time. One player controls the blue L-piece and the other player controls the red L-piece. Both players control the two neutral pieces. At the beginning of the game, the pieces are arranged on the board as follows:
Rules
To move: Pick up your L-piece and place it in a different way on the board. The L-piece can be rotated and flipped. The L-piece should be moved so that it covers at least one cell of the grid that was not covered by it immediately before it was picked up. Then, you may optionally move one of the neutral pieces to a different location on the board. Pieces are not allowed to overlap other pieces and may not hang off the side of the board. You may not move a piece on top of another piece.
To win: A player wins when their opponent is unable to move their L-piece on their turn.
Strategies
- Fundamentals: There are six fundamental ways an L-piece can be placed on the board. All other L-piece placements are rotations or reflections of these six. In every winning position, the loser will have their L-piece touching the edge of the board. 22/29 of winning positions involve the opponent's L-piece being trapped in the upper left hand corner, with the long side of the L on the left edge of the board.
Variants
- Misere: The objective is to force yourself into a position where you are unable to move your L-piece.
- Sudden Death: Players are allowed to move both neutral pieces in a turn.
- Scoring: The four squares in one corner of the board are marked so that every time the L-piece touches one of the four corners, a point is scored. If you block your opponent from placing their L-piece, five points are awarded and the game resets to the starting arrangement of pieces. The winner is the first player to reach an agreed total.
- Symmetry: The rules are the same as the classic game, except that in order to win, one must place their L-piece so that it is symmetrical to the opponent's L-piece.
- Pieces: The number of neutral pieces on the board can be changed to one. The same rules of the classic L-game apply.
- Required Movement of a Neutral Piece: Make moving a neutral piece mandatory for each turn.
- Initial Position: Players can change how the board is initially set up.
Pictures
References
Pritchard, David. Brain Games. New York: Penguin Books, 1982.
Links
GamesCrafters
Alex Kozlowski (Solving, Backend)
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Cameron Cheung (GamesmanUni GUI)