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This is an interesting game, very good idea for the playing mechanics. But the description is difficult to understand. If I got it right:
A player may either move their king or one of their stones. There is no capture, one can move only to empty squares. The king, if attacked, moves like a normal king (like fers or wazir). If not attacked, he may leap to any empty and not attacked square.
Stones move like wazir, fers, dabbabah, alfil or knight. A stone can move like X if a stone of any color or the friendly king is an X's move away. E.g. white stone on a3, white king or any stone on a4: the stone a3 can move like wazir (to a2 or b3).
If a king is on a square an opponent's stone could move to, the king is attacked.
Is this checkmate in 3?
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