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) 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.)

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.

thanks, Leroy Quet

I noticed yesterday a problem with the rules as-is if the number of players is even. For, with an even number of players, most squares filled with any one color/symbol will be isolated.

So, I suggest the rule-change that, if possible, a player must fill an empty square adjacent to the previously filled square (by the previous player) in the directions of up, down, left, right, OR DIAGONALLY.

With this rule-change, even if there are an even number of players, and even if the grid is completely filled in by only one connected sequence of squares (any 2 consecutively filled squares are immediately adjacent to each other in the grid), it is still possible that there will be islands of more than one square.

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.

And I did not mention an obvious point in my original post: the game continues until each square of the grid is filled in.

thanks, Leroy Quet