## Tuesday, September 15, 2009

### Dot Labeling And Connecting Game

This is a game for any plural number of players.

First, draw an array of n-by-n dots, which are the vertices of an (n-1)-by-(n-1) square grid. I suggest an n of at least 9.

Each player corresponds to a color or symbol (such as a number or letter or something else).

Players take turns. On each move a player connects two different dots (not necessarily in the same row or column) with a straight line-segment, then labels ANY unlabeled dot with ANY player's color/symbol. The two dots connected by the line-segment must not have been connected together in a previous move, although they may have been connected to other dots earlier in the game.

The line-segment must terminate at the two dots, and must not pass through any intermediately positioned dots or through any other line-segment.

As soon as all dots are labeled (after n^2 moves), the game is over.

Each player gets a point for each "group" of dots with the player's color/symbol, where each group contains at least two dots connected by a line-segment. A player only gets one point for each group of dots where every dot of that group -- a group of all dots of the same symbol/color -- is accessible by traveling along the line-segments from dot to dot of the same color/symbol.

If two dots of a player's color/symbol(#) can only be connected by traveling through a dot of another player's symbol/color, then the two dots of color/symbol # are considered to be in separate groups.

(There is graph-theory terminology for what I am trying to express, but I don't feel like looking up what that is.)

(And remember, each group that earns a point for a player must contain at least two dots of the player's symbol/color.)

The player with the most points wins.

Thanks,
Leroy Quet