Reflex Chess was invented in the 1880's by William Geary and B. J. Laws, and was reviewed in the May 1907 issue of Chess Amateur. It has been used primarily as a problem theme.
orthodox chess rules apply, except that the winner is the player whose king is checkmated. If a move gives mate, then the player must make such a move.
Variant: If a player indicates to his opponent that a move will lead to checkmate (in a specific, reasonably small number of moves), the opponent must make the move. However, if the move does not lead to checkmate (in the specified number of moves), then the opponent wins.
(Taken from The Encyclopedia of Chess Variants by David Pritchard)
(From The Problemist iii 1930)
First problem: Bb1 (threat Rg6)
Second problem: f4 (threat Re4)