## Friday, September 19, 2008

### Contiguous: Another Grid Game

Here is another simple game of mine (probably unoriginal) which is
played using an n-by-n grid drawn on paper.
(I would suggest an n of at least 5 or 6.)
Game is for any number of players >=2.
Each player uses a different colored pencil/pen, or each player uses a
different symbol (o, x, #, etc).
Players alternatingly take turns filling one square of the grid each
turn with either their color or symbol.
The square filled must, before being filled, be empty.
The square filled must be immediately adjacent to (in the direction of
either up, down, left, right, or diagonally) the most recently filled square
(which was filled by the previous player), if possible.
If no empty squares are adjacent to the last filled square, any empty
square in the grid can be filled.
(And any square can be the first filled square of the game.)
The game continues until each square of the grid is filled in.

What is interesting about this game (besides any beautiful designs
which result...) is the scoring.
Each player's score is the product of the numbers of squares in the
"islands" formed of their colors/symbols.
An island is any contiguous group of squares formed of one
color/symbol and surrounded completely by squares of other
colors/symbols (or by the edge of the grid).
So, the number of terms in the product making up a player's score is
the number of islands of a player's color/symbol.
Example (n=5) completed game:
x o # # x
# o x x o
x # o x #
o x o # o
# x o # x
Scoring:
x: 1*1*3*1*2*1 = 6.
o: 2*1*3*1*1 = 6.
#: 2*1*1*1*1*2 = 4.
So x and o have tied for first place.
Note:
If you have, say, 2 contiguous symbols of yours separated by one empty
square from, say, 4 contiguous symbols of yours, it would *not* be at
your advantage to place a symbol of yours in the empty square between.
For with someone else's symbol in the separating square, you would
have 2*4 =points for the 2 islands. But with the separating square
filled with your symbol, you get 2+1+4 = 7 points for the one larger
island.

Whether two diagonally-adjacent squares of the same color/symbol are
to be necessarily considered as part of the same island or not, I
leave for the players of this game to agree amongst themselves.

thanks,
Leroy Quet