Nimbler Otter

"Nimbler Otter" is a game with two players, human player A against human or computer player B, on a 16 cell board, using as pieces, the numbers 1 to 16. When it is B's turn, if you want the computer to play instead of a human, click the green button "B plays".

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 or she chooses a number between 1 and 16 from the list on top (to select a number, touch it) and puts it into one of the board cells (to place on the board a piece just selected, touch the board cell you want). Then it is player B's turn. He or she chooses a number 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 numbers 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 at the bottom 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.

Feature: This game, very simple in its design and rules (16 cells, 16 pieces, 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.

Buttons:
"rules" shows the rules of the game.
"new" starts a new game.
"A path." shows A's best path.
"B path" shows B's best path.
"back" goes back one move.
"random" fills a random board for various studies.
"test" fills a board with 7 pieces and cells remaining. It shows a configuration where B's only good move is particularly not intuitive.
"B plays" makes the computer play instead of B. When there remain only 7 pieces or less, the computer carries out an exhaustive analysis. With 7 pieces left, on a mid-range phone or tablet it takes approximately half a minute.

Strategy: there is an optimal strategy for A. It is left to you to find it.