Game Highway / Nimbler otterBuild the shortest path in a square 

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Player A plays against player B
Player B can have the computer play instead of him or her (except sixth and eighth moves), but can also play himself or herself.
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result:

Rules of game:
"Highway" is a game with 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 "Apath"), 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 "Bpath").
Sequence: Player A begins. He or she chooses a digit between 1 and 16 from the list on top and puts it into one of the cells of the board. Then it is player B's turn. He or she chooses a digit among those not yet used, and puts it into a cell still empty. 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 "Apath") is a sequence of seven adjacent cells (adjacent by sides, not by corners), starting from the top left and ending at 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 "Apath" with the smallest value. A path of player B (a "Bpath") 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 "Apath" has value 48, and the shortest "Bpath" has value 51, so A won.
Features of the game: This game, very simple in its design and rules (16 cells, 16 "pawns", 20 paths per player), leads nonetheless to a surprising complexity: 400 million billion billion possible games. It displays the characteristics demanded from a good game: simplicity of 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)
* In 2015, it was proved that A wins all the time, if he plays well.