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Checkless Chess. No piece may cross a square where it gives check. (8x8, Cells: 64) [All Comments] [Add Comment or Rating]
Ben Reiniger wrote on 2012-10-06 UTC
Rodrigo, I think the idea is that if after white's move, black's only response will put white in (non-mate) check, then that black move is illegal, so black is in fact in checkmate, and white's move was legal.

Then, what happens if black's only response is to put white in a similar position?  This is the "paradox" that is referenced.