Naked Diagonal

About

Naked Diagonal is a two-player game. A square board of any size is used. The north and south board edges are colored red. The west and east edges are colored blue. The board is initially empty. The two players, Red and Blue, take turns placing their own stones onto unoccupied points on the board, one stone per turn, starting with Red. Passing is not allowed, but if you don't have an available placement, your turn is skipped. The goal for each player is to form an orthogonally interconnected path of stones of his color connecting the two board edges of his color. Placement restrictionsPlayers are not allowed to form a naked diagonal or a naked diagonal-equivalent area. A "diagonal" is comprised of a pair of diagonally adjacent, like-colored stones. If no like-colored stone is adjacent to both of them, they form a "naked diagonal". An "empty area" is a group of orthogonally interconnected, unoccupied points (not necessarily maximally inclusive). An empty area is "naked diagonal-equivalent" if there is no possible sequence of placements, by either or both players, which can fill the area without forming a naked diagonal somewhere along the way. BAD - Banned and disconnectedImagine an empty area in which one player, say Red, has no available placements. Red is "banned" from that area. Blue may have available placements in the Red-banned area, but there is no possible sequence of blue placements with which Blue can fill the area without creating a naked diagonal somewhere along the way. Blue is "disconnected" in the area. Such an area is "banned and disconnected" (BAD). All but two known naked diagonal-equivalent areas are BAD areas. Design notesNaked Diagonal exists to demonstrate some connection game principles. (And conversely, the principles themselves comprise a game.) Naked Diagonal may not be a game that anyone would ever want to play, although there's nothing stopping you. Naked Diagonal has a sister game, Candy Necklace, which also explores properties of connection games.

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