Some Chess Problems

Please refer to the given chess position here. http://home.comcast.net/~joyner.david/wdj/chess/Elkies05_files/Elkies05D01.gif

White has to draw against the battery of black pawns assisted by their bishop. How to accomplish the task?

Answer:

White hopes to trade his rook for Black's connected central pawns and reach a theoretical draw against the h-pawn and "wrong" bishop. First, 1 Re5? e3 2 Kg4 e2 3 Kxf4 e1/Q? 4 Rxe1+ Kxe1 5 Kf3! Kf1 6 Kg3 h5 (else 7 Kg2 or 7 Kh2 and draws) 7 Kh4 would draw as planned, except for 3 ... Bh2+! winning. Note that the position after 6 Kg3 is a mutual zugzwang: were it White's turn he would lose quickly after 7 Kf3 Bf2(h2) or 7 Kh3 Kf2 8 Kg4 Kg2 and 9 ... Be3. This explains Black's play against the second thematic try:1 Rc4! e3 And now 2 Rxf4!? e2 3 Re4 e1/Q+! 4 Rxe1+ Kxe1, and this too is a mutual zugzwang, White losing as before with 5 Kg3 Kf1, 5 Kh3 Kf2, or 5 Kg4 Ke2! 6 Kg3 Kf1. But had Black played here 2 ... Kd2 3 Rxe2+ Kxe2 then White would instead prevail by zugzwang with 4 Kg4! and now 4 ... Kf1(Ke3) 5 Kg3! and 4 ... Ke1 5 Kf3! draw as in the first thematic try, while 4 ... Kf2 blocks the Bg1 and thus abandons the remaining pawn to 5 Kh5. Hence the solution: after 1 Rc4 e3 White interpolates 2 Rd4+! Kc2 Or 2 ... Kc1; blocking the e-pawn with 2 ... Ke1(e2)? only helps White. Only now does White play 3 Rxf4 e2 4 Re4 Kd2 Note the threat 5 ... Be3! winning outright-- if 5 Re8 Be3 6 Rd8+ the Black king runs to h5 or h7 and then the e-pawn promotes. 5 Rxe2+ Kxe2 6 Kg4! And White draws by the progressive zugzwang analysis above. Remarkable depth with only four men in play!