Hello Doctor Z, You are on the right track, but one of your variations doesn't work (I think). See my comments below in your message. Richard ----- Original Message ----- Hello All, Doctor Z is ready to operate. My solution: variation #1 1. Rg4+ fxg4 2. Qg6+ Kh8 3. Qh7++ * Good job! variation #2 1. -Kh8 2. Qxh6++ * Also looks good. variation #3 1. -kh7 2. Qg6+ Kh8 3. Qg8++ * what about the black rook on f8? 3... Rxg8! variation #4 1. -Qg5 2. hxg5 fxg4 3. Qg6+ Kh8 4. Qh7++ * Also looks good, very good!