Rules of game:
"Highway" is game opposing two players, player A against player B, on a 16 cell board, using as "pawns" the numbers 1 to 16.
Goal: Player A wants to build a path from the top left cell to the bottom right cell (an "A path"), with the smallest possible value. Player B has the same goal, with a path going from the bottom left cell to the top right cell (a "B path").
Sequence: Player A begins. He/she chooses a digit between 1 and 16 and writes it into one of the cells (including overwriting the initial letters A's and B's, which are only there to indicate the paths' ends). Then it is player B's turn. He/she chooses a digit among those not yet used, and writes it into a cell still empty (including those with letter's). Then it is A's turn again, and so on until the sixteen digits have been put into the sixteen cells.
Paths: A path of player A (an "A path") is a sequence of seven adjacent cells (adjacent by sides, not by corners), starting from the top left and ending to the botton right. There are 20 such paths. The value of a path is the sum of the numbers it contains. The program computes automatically the best path for A, that is the "A path" with the smallest value. A path of player B (a "B path") goes from the bottom left to the top right. There are also 20 of them. And the programme computes the best.
Winner: The winner is the player who built the shortest path, that is the path with the smallest value. Here is an example:
the shortest "A path" has value 48, and the shortest "B path" has value 51, so A won.
Interest of the game: This game, very simple in its design and rules (16 cells, 16 "pawns", 20 paths per player), leads to a surprising complexity: 20 000 billion possibilities! It displays the characteristics asked from a good game: simplicity of the rules, necessity to think, unexpected flips of situation, limited duration, unknown (so far) optimal strategy to surely win.
Copyright : André Cabannes (patents INPI & OMPI, 1998)
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