Hex KB 2009

Hex KB is a two player game, played on a hexagonal board with two red border segments, two blue border segments, and a green "portal." The "KB" stands for Klein bottle, an unusual, four dimensional shape. The Hex KB board is a Klein bottle, or more precisely, a Klein bottle with a hole in it. The hole perimeter is divided into four segments, alternating in color between red and blue, and is stretched outward, flattening the Klein bottle and forming an outer perimeter.

The two players, designated Red and Blue, take turns claiming unoccupied cells on the board, one cell per turn, by adding stones of their own color to the board.

The two green "portal frames" are considered to be coincident. So when you place a stone on a portal frame cell, you must also place a stone on the corresponding cell in the corresponding portal frame while it is still your turn.

Draws cannot occur in Hex KB. Furthermore, if the board is completely filled with red and blue stones (in any proportion of red stones to blue stones), there will always be a winning solution in one color but never in both colors simultaneously.

Path types Simple connecting path: A path of like-colored stones that connects the two border segments of the stones' color, and which doesn't pass through the portal. Single transit connecting path: A connecting path that passes through the portal once. Double transit connecting path: A connecting path that spirals through the portal twice. Portal loop: A loop of stones that passes through the portal. Border segment cells: Cells in a border segment can be used as part of a path of stones which are the same color as the border segment.

Object of the gameTo win, you must meet at least one of the following three criteria:

1. Simple connecting path, passing through the portal net zero times. 2. Portal loop and single transit connecting path (two paths total). 3. Double transit connecting path.