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Refusal Chess. Refuse your opponent to make certain moves. (8x8, Cells: 64) [All Comments] [Add Comment or Rating]
Ben Reiniger wrote on Wed, Oct 30, 2013 05:52 AM UTC:

It sounds like perhaps you're misunderstanding the rules. Each turn a player attempts to make a move as usual. If the opponent wishes, they can force the player to retract that move and make another.

What you describe sounds like No-Chess
http://www.chessvariants.org/other.dir/no.html
For that game, I think the answer to your question should be "yes". In particular, white can "refuse" some impossible move.