[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

Re: [pbmserv-dev] A three-player connection game


On a board like this, there are three simple ways to form a non-trivial loop,
each of minimum length n:

  . . x . . .        . . . . . .        . x . . . .
   . . x . . .        . . . . . .        x . . . . .
    . . x . . .        . . . . . .        . . . . . x
     . . x . . .        . . . . . .        . . . . x .
      . . x . . .        x x x x x x        . . . x . .
       . . x . . .        . . . . . .        . . x . . .

Vert Horz Diag

This three-player game has also recently been discovered by Bill Taylor (kiwibill) who calls it Porus Torus.

P. S.  Your homework assignment (2 stars): Invent a connection game on the
Klein bottle.

Divide the klein bottle surface into a finite number of similar cells (hexagons plus six pentagons, as per the sphere?). Moving in a cell colours the cell faces on both sides of the surface. Then either:

a) Play Projex; or
b) Assign two maximally distant cells to one player and play Antipod.

These are the only two connection games I know of that are totally independent of edges.

camb