Pythagoreic Halma can be played by 2-4 players. The goal is to transport your pieces to the opposite side of the board and occupy the eight central squares on the last rank. When a piece is placed there it loses its movability. In the first stage players take turns to drop pieces on the first rank. When all seven pieces have been dropped they may move one step according to their movement design, or jump over any piece in the same direction, provided that the destination square is empty. Diamonds move diagonally. Squares move orthogonally. Circles move in all forward directions, and sideways. Triangles move diagonally forwards or straight backwards. Pieces are allowed to jump back to the previous square if they jump into the margin. This implies that triangles, in this special case, may move contrary to their movement rule. However, as it is only a take-back move it doesn't affect the game.
Pieces cannot capture. It's not allowable to place a piece on the side of the board (except for the destination squares). However, it's allowable to jump via the side of the board. It is permissible to move along the first rank and to place a piece on the initial squares so long as this piece hasn't left the initial squares. Multiple jumps are allowed and can be discontinued. It's only permissible to jump back to where you came from if the piece has landed on the margin (except the destination squares).
In Pythagoreic Halma with "advanced rules" a piece may jump over multiple squares, as long as a single piece occupies the center square along the jump, and the other squares are empty. If the jumping piece is a circle, and the jumped piece is an enemy circle, then the latter is sent back to the first rank (or second if there are no free squares in the first). If the "send-back" jump will end in the margin (except the destination squares), then it is prohibited (a rule introduced in this implementation). A circle which is positioned on the first or the last rank is not sent back.
If an enemy piece, other than circle, occupies a position adjacent to a piece on any of the initial squares, then the latter is forced to immediately jump out (see below).
Note! When having performed a jump then you must always acknowledge that the jump sequence has ended by again lifting and dropping the piece on the same square.
If you have started jumping in the margin and realize that you cannot find your way out then you must go back the same way, since you are not allowed to discontinue the move, and place a piece in the margin. The same applies to triangles when they have jumped out into the margin and cannot find their way out. It's then allowable to jump back the same way, although this movement direction is normally not allowed for triangles. Should you end up in an eternal loop that goes back and forth, then the move is prohibited and must be taken back. This corrective movement, which only involves movement in the margins, is in practice never performed but is added due to technical reasons.
I have added an additional outjump-rule to prevent blocking of the goal-squares: if an enemy piece, other than circle, occupies a position adjacent to a piece on any of the initial squares, then the latter is forced to immediately jump out over the enemy piece, provided that the movement rule of the piece allows this and provided that the jump does not end in the margin. Circle's cannot cause outjump. They can easily make it to the goal squares anyway.
In Pythagoreic Halma with "simple rules" you can only make short jumps, and there is no "send-back" rule.
Pythagoreic Halma, conceived by undersigned, is really only a variant of a game invented by
The difference between Platonic Halma and Pythagoreic Halma is (1) in the latter there is one piece less (there is only one Diamond) (2) the board is smaller (9x9), and (3) circles may not move in the backward directions. Although the circle is only half as strong as in Platonic Halma, it is still the strongest piece.
Place your pieces so that they can be jumped by your own pieces and thereby can facilitate the transportation of your own pieces. If possible, try to obstruct enemy pieces. If advanced rules are used, learn to master the circle, which is an important piece due to its send-back capability.
What about the name "Pythagoreic Halma?" The pieces are reminiscent of Plato's and Pythagoras's perfect mathematical Forms, that enter into Physis from their world of eternal Forms, symbolized by the margin. In this game the antique and medieval notion of the "four elements" are reflected in the four types of pieces. Also the triangle, so important in Plato's thinking, is represented.
You can download my free Pythagoreic Halma program here, (updated 2006-02-23) but you must own the software Zillions of Games to be able to run it.
© M. Winther 2006