Hello All, Doctor Z is ready to operate. My solution: 1. -Re1 (Rook attacks queen.) 2. Qxe1 (Queen takes rook.) Nxf3+ (Knight takes bishop.) 3. Kh1 Qh2++ 3. Rxf3 (Rook takes knight.) Qxe1+ (Queen takes queen and checks.) At best, white exchanges a bishop and queen for a rook and knight. This gives black a winning endgame. Edward