The game of Flaxman

Flaxman is a chess-like game I invented in my teens. The allusion is to the "man with a line of flax" in Ezekiel 40:3, who measures the temple, because measurement is central to the game, with a nod also to the 19th-century sculptor John Flaxman, who made chessmen in collaboration with Josiah Wedgwood, and to the famous Gengleston Herbert Flaxman, a Chess king of the early 15th century, whose accomplishments are outlined in the unfinished "Chess Monograph" of the young C. S. Lewis.

In the simplest version of this game, each player has three pieces, a King and two Soldiers. (You can use chess Kings and Knights). The game is played on a 7-by-7 grid, but the pieces are positioned on the corners rather than in the squares, as in Chinese chess, so there are only 36 positions. This is the starting layout.

The basic concept behind the game is that no piece has a fixed move. Rather, each piece's move is defined by two other pieces. If A's move is defined by B and C, that means that A can jump to any new position such that the distance between the new position and the old position is equal to the distance between B and C.

In three-piece Flaxman, each piece's move is defined by the other two pieces of the same color: the King's by the two Soldiers, and each Soldier's by the other Soldier and the King. So these are the possible opening moves for White, for the King:

for one of the Soldiers:

and for the other Soldier:

Let's say that after two rounds, the board looks like this:

The two White soldiers are three spaces apart, so the King can move three spaces vertically or horizontally. We say that his move is (3, 0), meaning three spaces vertically and zero spaces horizontally or vice versa. However, if he moved three spaces to the right, he would be moving into check, which is forbidden as in chess, so three spaces down is the only possible move for the King.

Now look at the Soldiers. The King and the left Soldier are at the corners of a 3-by-1 rectangle, so we say that the right Soldier's move is (3, 1): He can move three spaces vertically and one space horizontally or vice versa. Here are his possible moves:

The left Soldier's move is (4, 3) -- but this is a very special case. By the Pythagorean theorem, the diagonal of a 3-by-4 rectangle is 5, so this Soldier is also allowed to make a move of (5, 0). This special move -- moving (5, 0) when you have a move of (4, 3) or vice versa -- is called a Pythagorean leap. So the right Soldier's possible moves are as follows:

He can use the Pythagorean leap to capture one of the Black soldiers -- but how does capturing work in this game? If one of the Black pieces were removed from the board, the moves of the other two Black pieces would no longer be defined -- so captured pieces are not removed. When a piece is captured, it (1) swaps places with the piece that captured it and (2) becomes immobile, a Prisoner instead of a Soldier. (You can use a chess Rook to represent a Prisoner.) Prisoners cannot move, but their position can still be used to define the moves of the other pieces.

After the capture, the board looks like this:

Black's next move is forced. The Prisoner cannot move, but neither can the other Soldier. The Black Soldier's move, defined by the King and Prisoner, is (5, 1), but there is no space on the board that is that distance from the Soldier. When a piece cannot move because the two pieces that define its move are too far apart, we say that it is "pinned." Only the King can move, and his move is (4, 2). There are two positions on the board that are (4, 2) from the King, but only one of them is allowed because the other would mean moving into check (shown by the blue line below).

So Black makes the only possible move, and the board now looks like this:

So that's how moving and capturing works. There are just two more rules to discuss.

Freeing Prisoners: "Capturing" a Prisoner frees him, changing him back into a mobile Soldier. As in a capture, the freed Prisoner swaps places with the piece that frees it. You will normally want to free your own Soldiers, but it also possible to free your opponent's Soldiers, and this may be worthwhile in certain situations.

King's capture: The King, and only the King, has the option of capturing one of his own Soldiers. This works exactly like a normal capture: The King and Soldier swap places, and the Soldier becomes a Prisoner. This may sometimes be necessary in order to get out of check.

As in chess, checkmate is a win, and stalemate is a draw. If it's your move and all your mobile pieces are "pinned," that's considered a stalemate, too.

There's a more complicated version of the game, called Witchy Flaxman, but the simple version is usually quite complicated enough for beginners. It takes quite a bit of practice to become familiar enough with the rules to be able to think several moves ahead.