## Thursday, September 18, 2008

### Next To Something Else: Grid Game

Here is another simple game.
(Again, not a lot of math, but still the kind of game which might be
interesting to analyze mathematically.)
2 players.
You have an n-by-n grid, where n is even.
Each player has a different colored pencil/pen (or one player has a
pencil, the other a pen).
Players take turns writing integers into yet-unfilled squares. The
integer a player writes in a square is the number (0 to 3) of adjacent
squares (above/below/right/left) which have, at the time the player
writes the integer, integers written in them which are of the player's
OWN color.
A player can only write an integer in a yet-unfilled square which
either is on the border of the grid or is immediately adjacent
(above/below/right/left) to a square filled in with the player's
OPPONENT'S color.
(Unlike with "Next To Something: Grid-Game", in this game a given player can
fill in a square in any of the 4 empty squares adjoining his/her
opponent's color or in any empty square along any of the 4 borders of
the grid, not just in 2 of the empty squares adjoining an opponent's
square or along 2 of the grid's borders.)
If a player cannot move, because there are no empty squares next to
his/her opponent's color, he/she simply skips his/her move.
Play continues until the grid's squares each have an integer written
in them.
The winner is the player whose total sum of all his/her integers is
greatest.
Any winning strategies?
thanks,
Leroy Quet