The answer is for white to play R-g7.  If black plays R-f5, then R-g8 leads to mate. If black plays R-b8 instead, then R-a7 is checkmate.

I hope you found the answer. Look for another of these challenging chess puzzles in my next post! If you would like to begin having these puzzles sent to you, just add your email address in the “Subscription Options” box and click “Subscribe.”