There are versions of Ataxx where piece may jump are only in horizontal, vertical and diagonal directions, without the 8 destinations of the "horse jump" in the Chess game
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Jump to corners
The four corners of the destination square are not available.
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Ataxx with horizontal and vertical jumps only
Only horizontal and vertical jumps allowed.
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Ataxx without jumps
Jumps are not allowed
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Ataxx with horizontal and vertical moves only
Only horizontal and vertical moves/jumps allowed.
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Drop Moves
You can play with drop moves. This variant of Ataxx has other name - Blobs. If slide and jump moves are unavailable a piece may be dropped onto any square on the board. No enemy pieces are converted.
