SELECTED COMPOSITIONS

GEORGE GRATZER¨

1 2 GEORGE GRATZER¨

If you done it, it ain’t bragging. Baseball great “Dizzy” Dean

1. Introduction

This is the cover of the magazine Magyar Sakk´elet(Hungarian Chesslife), the official organ of the Hungarian Chess Federation, from May 1954. It records the last chess game I played in a tournament. (I am the youngster on the right side of the picture.) SELECTED CHESS COMPOSITIONS 3

This is how the story starts about my chess compositions. I am a mathematician, and as such I am not used to writing in the first person singular. But if I want the story told, I have to tell it myself. Almost everybody in this story is dead, most long dead. When my picture appeared in the , I was about to graduate from grade 12. The team I played for, Tipogr´afia (Typography), just won the Budapest championship. The leader of our team was asked to write an article for the magazine about our team, so he asked us to look over the games we played in this tournament, and look for positions in which we were clever, so he can write them up. It was a big chore to look over the thirty or so games. The result was extremely disappointing. Even though I rated 85%, every win was due to an error of the opponents. I decided that the time I spend on chess would be more satisfying if I created chess problems—these are absolute and not illusory, not dependent on your opponents ignorance and psychology. Dr. Jen˝oB´an(1919–1979), one of the chess masters at the , introduced us to chess compositions, especially endgames (white plays and wins or draws). I figured that if I compose endgames, and I state that white wins (or draws), these ought to be absolute, and not dependent on mistakes by the opponent. I started studying endgames; you have to be familiar with thousands of them to create original ones. My second mentor was Gy¨orgyP´aros(1910–1975). Unquestionably the world leading in .1 He taught me how to aim at uncluttered positions, few pieces, and elegant ideas. P´arostold me the story of one of his most famous compositions; how he struggled with the idea for years, and how he woke up one morning and set up the position on his chess board. And that is why I quit after about two years. The subconscious work necessary for success in chess compositions competed against the same for mathematical research, and I had to give one of them up. I look back at this period, 1954–56, with great satisfaction. For this time period, my endgame #11 was officially placed the second best in Hungary—which is not bad because I was so young and just starting. And the one placed first proved to be defective! Acknowledgement. Having moved in the last 50 years to two new countries, it is not surprising that I have no record of my chess compositions. M´ariaHalmos did all the work to find them, and I do believe that she found most of them. J´anosMikitovics (JM)—the author of the splendid Website: Hungarian Chess Composers: http://www.magyarsakkszerzok.com/index.html—went through my compositions and sent me a long document, analyzing them. He also took the time to educate me about the technical advances that have happened, especially, Fritz (I now have version 11) and the Knowledge4IT Website. Another huge advance is the Nalimov endgame databases, now complete up to 5 pieces (consider that my Composition #1 had only 5 pieces), and covering all the 6 piece positions without pawns.

1In a both sides are cooperating to black. The first move is made by black. So in a “helpmate in two”, black moves, then white moves, then black moves again, and finally white black. 4 GEORGE GRATZER¨

2. Picking favorites I agree with MJ. If you want to see only three chess compositions of mine, pick the endgames No. 1b, No. 11 and the helpmate No. 13. SELECTED CHESS COMPOSITIONS 5

3. Chronological listing

1a. 1954 Hungarian National Endgame Competition Sixth place Magyar Sakk´elet 1954, issue 11/12, p. 285 (revised)

White draws This was my first endgame composition; I was 18. It was published in 1954 in Magyar Sakk´elet, so it participated in the 1954 Hungarian National Endgame Competition, placing sixth. 6 GEORGE GRATZER¨

Solution (Magyar Sakk´elet 1954, issue 11/12, p. 285): 1.Kg6!(1. g4? d5 2. g5 d4 3. g6 d3 4. g7 Bc4 — black wins) 1. –, d5 2. Kf5 d4 3. Nd7! (3. Ke4? d3 4. Ke3 Ke1 —black wins) 3. –, d3 4. Nb6! (4. Nf6? Bc6 —black wins) 4. –, d2 5. Nd5 Ke2 6. Nc3+ (6. Kf4? Bc6 7. Nc3+ Kd3 8. Nd1 Bg2: — black wins) 6. –, Kd3 7. Ne4! d1Q 8. Nf2+—. 5. –, Kg2: 6. Nc3, Kf3 7. Ke5 Ba4 8. Kd4 Bc2 9. Nd1 Ke2 10. Nb2 —draw SELECTED CHESS COMPOSITIONS 7

1b. OTSB Nyeviczkey Memorial Competition First prize (revised) Magyar Sakk´elet 1956, issue 11/12

White draws Two years later, I composed this endgame. This leads to the opening position of 1a, when in move 6 black appears to capture the white with Bb5. 8 GEORGE GRATZER¨

Solution (Magyar Sakk´elet 1956, issue 11/12): 1. b7 Rh4+ 2. Kg7 Rg4+ 3. Kh8: Rg8+ 4. Kh7 Bc4 5. b8Q Rb8: 6. Nb8: Bb5 —now continue as in #1, white draws. SELECTED CHESS COMPOSITIONS 9

2a. OTSB 1954 Hungarian National Endgame Competition (revised) Second HM Magyar Sakk´elet 1954, issue 12, #82

White wins 2b.

White wins 10 GEORGE GRATZER¨

Solution 2a (Magyar Sakk´elet 1955, issue 3): 1. Bh4:+!! (1. Bc7+? d6!! 2. Rg8 Kf2 3. Rf8 Ke1 4. Rg8 e2 5. Ba5 Kd1 or 1. Rb8 e2 2. Ba5 h3 —white cannot win;) 1. –, Kh4: 2. Rh6+, Kg3 3. Rh1, Kg2 4. Rb1!, Kf2 5. Kd3, e2 6. Kd2, Kf3 7. Re1!, d6 8. Rg1!, Kf2 9. Rb1!, Kf3 10. Re1, d5 11. Rg1!, Kf2 12. Rb1!, Kf3 13. Re1, d4 14. Rg1!, Kf2 15. Rb1!, Kf3. 16. Re1, d3 17. Kd3:, Kf2 18. Kd2, Kf3 19. Rg1, Kf2 20. Rb1, Kf3 21. Re1 —and so on, white wins.

Solution 2b Same as that of 2a, starting with move 2. SELECTED CHESS COMPOSITIONS 11

3. Magyar Sakk´elet 1955, issue 1, #90

White wins 12 GEORGE GRATZER¨

Solution (Magyar Sakk´elet 1955, issue 4): 1. cb6:, Rb6: 2. Qd8+, Ka7 3. Qd4!, g5 4. Kg2!, g4! 5. Kg1!, f3 6. Kf2, h3 7. Kg3 —and so on, white wins. SELECTED CHESS COMPOSITIONS 13

4. Magyar Sakk´elet 1955, issue 4, #1863

Helpmate in 3 (version) a. The diagram b. Move white from b3 to g5 14 GEORGE GRATZER¨

Solution (Magyar Sakk´elet 1955, issue 6): a. 1. Nb4:, g8N 2.Nc6, b4! 3. Nd8, Ne7 —checkmate.

b. 1. Bc1, g8B 2. Bg5:, Bf7! 3. Bd8, Be6 —checkmate. SELECTED CHESS COMPOSITIONS 15

5a. Magyar Sakk´elet 1955, issue 5, #105 (revised)

White wins 5b. Magyar Sakk´elet 1955, issue 5, #106 (revised) BTSB 1956 International Endgame Competition Fourth prize Magyar Sakk´elet 1956, issue 11/12, #106

White wins 16 GEORGE GRATZER¨

Solution 5a (Magyar Sakk´elet 1955, issue 8): 1. a6 h3 2. Nf3! (2. a7? Bd5: 3. Kd5: h2 4. a8Q h1Q+ 5. f3 Qe1: 6. Ke5: Qg3+ 7. Kf5 Qf4+ 8. Kg6 Kf2 9. Qe4 Kg3 10. Kh5 Kg2! 11. Qf4: gf4: 12. g5 Kf3: — draw.) 2. – Kf3: 3. a7 Bd5 4. Kd5: h2 5. Ke5:! Kg5: 6. a8B! —white wins. (6. a8Q? h1Q 7. Ke5: Kg4: 8. Qh1: —.)

Solution 5b: 1. Nc3 (1. a7? Bd4 2. Bb6: Bh8 3. Bc7 a3 4. Bd5 Bd5: 5. Kd5: a2 6. h8Q a!Q+ 7. f3 —easy draw) 1. –, Kc3 2. h7, Bd4 3. Bb6: Bh8 4. Bc7! (4. Bd8 a3 5. Bf6+ Bf6: 6. Kf6: a2 7. h8Q a1Q 8, Ke6+ d4 —easy draw) 4. –, a3 5. Bc7! a3 5. Be5+ Be5: 6. Ke5: h8B! —white wins. SELECTED CHESS COMPOSITIONS 17

6. With P. Bauer BTSB 1956 International Endgame Competition Nineth place Magyar Sakk´elet 1955, issue 6, # 116

White wins 18 GEORGE GRATZER¨

Solution (Magyar Sakk´elet 1955, issue 9): 1. Re2 d3 2. e7! d2! 3. Rd2: Re6 4. Rd7+ Kb6 5. Kc3! (5. Rd6? Kb5: 6. Re6: —stalemate; 5. Kc4? Re7: 6. Re7: —stalemate) 5. – Kb5 6. Kd4 Kc6 7. Ra7 Re1 (7. – Kb6 8. Kd5 Re1 9. Rd7 —wins) 8. b5+ Kb5: 9. Kd5 Kb6 10. Rd7 Rd1+ 11. Ke6 Re1+ 12. Kf7 Rf1+ 13. Ke8 and Kd8 —wins. SELECTED CHESS COMPOSITIONS 19

7. Magyar Sakk´elet 1955, issue 7, #1933

Mate in 45 20 GEORGE GRATZER¨

Solution (Magyar Sakk´elet 1955, issue 10): 1. Na3+ Ka1 2. Nb1! Kb1: 3. Qd3+ Ka1 4. Qd4 Kb1 5. Qe4+ Ka1 6. Qe5 Kb1 7. Qf5+ Ka1 8. Qf6 Kb1 9. Qg6+ Ka1 10. Qg7 Kb1 11. Qh7+ Ka1 12. Qh8 Ka1 13. Qg7 Kb1 14. Qh7+ Ka1 15. Qh8 a6 16. Qg7 Kb1 17. Qh7+ Ka1 18. Qh8 a5 19. Qg7 Kb1 20. Qh7+ Ka1 21. Qh8 a4 22. Qg7 Kb1 23. Qh7+ Ka1 24. Qh8 a3 25. Qg7 Kb1 26. Qh7+ Ka1 27. Qh8 b5 28. Qg7 Kb1 29. Qh7+ Ka1 30. Qh8 b4 31. Qg7 Kb1 32. Qh7 Ka1 33. Qh8 e1Q+ 34. Ke1: Kb1 35. Qh7+ Kc1 36. Qh6+ Kb1 37. Qg6+ Kc1 38. Qg5+ Kb1 39. Qf5+ Kc1 40. Qf4+ Kb1 41. Qe4+ Kc1 42. Qe3+ Kb1 43. Qd3+ Ka1 44. Kd4 Kb1 45. Qd1+ — checkmate. SELECTED CHESS COMPOSITIONS 21

8. Magyar Sakk´elet 1955, issue 10, #1989

Mate in 4 22 GEORGE GRATZER¨

Solution (Magyar Sakk´elet 1956, issue 1): 1. g7! threats: 2. Qg6 checkmate and 2. gh8:Q checkmate. 1. – Rhe8: 2. g8N+ Rg8: 3. Nf6 —checkmate in the next move. 1. – Rce8: 2. gh:Q+ Rh8: 3. Ng7 —checkmate in the next move. SELECTED CHESS COMPOSITIONS 23

9. Magyar Sakk´elet 1955, issue 11, #2037

Helpmate in 2 On October 6, 1955, Gyula Neukomm organized a “composition with a theme” quick tournament. Time limit for creating the composition: 2 hours; time limit for judging: 1 hour. The theme: Helpmate in 2, and in the first move, the black takes the white queen. If the white queen (on e7) is removed or replaced by another piece, the compo- sition is incorrect; least obvious is the replacement with a , in which case, the unintended solution is 1. Kd5: Bf3+ 2. Kd6: Bb4 —checkmate. 24 GEORGE GRATZER¨

Solution (Magyar Sakk´elet 1955, issue 11): 1. Qe7: Kg2 2. Nd3 Bf3 —checkmate. SELECTED CHESS COMPOSITIONS 25

10. 1955 Competition of the Finnish Federation of Chess Composers Sixth place Magyar Sakk´elet 1956, issue 3, #189

White wins 26 GEORGE GRATZER¨

Solution (Magyar Sakk´elet 1956, issue 3): 1. c4! Bc4: (1. – Rd1 or f1 2. Ne3+ —white wins. 1. – Ra5 2. f7 Rf5 3. Ne3+ —white wins) 2. Ne3+ Kb3 3. Nc4: Kc4: 4. Bf3! Ra5 (4. – Rf1 or a6 5. Be2+ — white wins. 4. – Rb1 or a2 5. Be2+ and 6. f7 wins.) 5. Bg4 — white wins. SELECTED CHESS COMPOSITIONS 27

11. 1955 N´epszava First prize Magyar Sakk´elet 1956, issue 3, #186 Fourth Hungarian National Competition Second prize Magyar Sakk´elet 1957, issue 8/9, #242

White draws 28 GEORGE GRATZER¨

Solution (Magyar Sakk´elet 1956, issue 3): 1. Na4+ Kb4 or b5 (1. – Kd5 2. Nb6+ Ke5 3. Nd7+ and so on perpetual or return to the main variant) 2. Rb6+ Ka4: 3. Bd7+ Nc6 4. Bc6:+ Ka5! (4. – Qc6: 5. Rc6 and 6. Rc1 —draw.) 5. Rb5+! (5. Bg2:? Kb6:! 6. Bd5 Kc5! — black wins.) 5. – Ka6 6. Bg2: Kb5: 7. Bf1!! Kb4 8. Kc2 — draw.

6. – a2 7. Rc5!! a1Q 8. Bh3: Qd1+ 9. Kc4 Qc2+ 10. Kb4 Qb2+ 11. Kc4 Qe2+ 12. Kb3! —draw (12. Kb4? Qe7! 13. Kc4 Qh4+ —black wins).

Similarly 9. – Qc1+ 10. Kb4 Qf4+ 11. Kb3! —draw. SELECTED CHESS COMPOSITIONS 29

12. OTSB 1956 Second prize Magyar Sakk´elet 1956, issue 7, #2155

Helpmate in 3

Solution: 1. Kf5 d8B 2. Ke6 e8R 3. Kd7 b8N —checkmate. 30 GEORGE GRATZER¨

13. Magyar Sakk´elet 1957, issue 5, #236

White draws

Solution (Magyar Sakk´elet 1957, issue 10): 1. e7! (1. b3? a3 2. e7. Rg3:+! 3. Kg3: Bg6: —black wins. 1. g7? Rd8 —black wins.) 1. – Re3 2. g7 Ba2 3. b3! Bb3: 4. e4! Be4: 5. Ne6! Be6:! 6. e8Q Bg4: 7. Kh4! Re8: 8. g8Q Rg8: —stalemate. SELECTED CHESS COMPOSITIONS 31

14. Magyar Sakk´elet 1957, issue 6, #242

White wins

Solution (Magyar Sakk´elet 1957, issue 10): 1. b5+! Kb5: 2. de:! (2. Be2+? Kc5 3. de: Rh3+ and 4. – Re3 —draw.) 2. – Ne7: 3. Be2+ Kc5! 4. Ne7: Rh3+ 5. Ka2! (5. Ka4? Rh4+ and 5. – Re4 —draw.) 5. – Be3 6. b4+! and 7. Hd5 (f5)+ wins. (1. de:? Ne7: 2. Be2+ Kb7! 3. Ne7: Rh3+ and 4. – Re3 —draw. 1. Ne7:? Ne5! 2. Be2+ Kb6 3. Ka4 Rh1 —draw.) 32 GEORGE GRATZER¨

15. Magyar Sakk´elet 1957, issue 12, #257

White wins

Solution (Magyar Sakk´elet 1958, issue 1): 1. Re4! (1. Ng1:? Bh4: —draw.) 1. – Nf3:! (1. – Nh3: 2. Re1:+ Ka2 3. Kc3: Nf4 4. Rdl —white wins.) 2. Ng1! Ng1: 3. Re1:+ Ka2 4. Re3! (4. Rg1:? —stalemate) 4. – Ka1 5. Bc3:! (5. Kc3:? Kb1 —draw.) 5. – Ka2 (5. – a2 6. Re3! —white wins.) 6. Re3 c3! 7. Kc3:! Kbl 8. Kb3! —white wins. SELECTED CHESS COMPOSITIONS 33

4. Cooks and comments 1a. This endgame was published without the white pawn on g2. Cook:2 1. Kg6 d5 2. Kf5 d4 3. Nd7! d3 4. Nb6 d2 5. Nd5 Ke2! 6. Nc3+ Ke3! — and black wins. This position, of course, today is part of the Nalimov database. JM observed that placing a white pawn on g2 eliminates the Cook.

1b. Because of the Cook for 1a, this also had to be revised. Just placing a white pawn on g2 introduces a Cook. There are many ways to go around it, I show two.

2. Originally, this was published in the form:

White wins Cook: 1. Rg6+! Kf3 (1. –, Kf2 2. Bxh4+ Ke2; 2. –, Kf1 3. Rb6 Ke2 4. Be7 Kd1 5. Bxa3 e2 6. Rxb2+-) 2. Rg1 Kd2 3. Kc4 Kc2 (4. –, d5+ 5. Kb3+-) 5. Rg2+ e2 (5.–, Kd1 6.Kc3+-) 6. Rxe2+ Kd1 7. Re1+ Kc2 8. Kb4 b1Q+9. Rxb1 Kxb1 10. Kxa3 —white wins. Easiest correction: drop the first move, see 2b. Alternatively, the rook’s access to the g file, as is done in 2a. This solution has the added advantage that in 2a the check on c7 seems very attractive.

2A Cook or Cook solution is an alternative way of achieving the goal, demonstrating that the composition is flawed. 34 GEORGE GRATZER¨

This endgame shows some limitations of even the best chess programs. Look at this position in this endgame:

White wins Even with unlimited time, Fritz 11 does not find the winning move: Rb1. Nor does Sigma Chess with HIARCS 12.1 MP. Apparently, this type of zugzwang3 is difficult for a computer program to analyze.

3A situation in a chess game in which a player is forced to make an undesirable or disadvan- tageous move. SELECTED CHESS COMPOSITIONS 35

5. Originally, 5a was published without the c2 pawn. Cook (JM): 1. a6 Bb1! 2. Kxe5 h3 3. a7 Be4 4. Kxe4 h2 5. a8Q h1Q+ 6. f3 Qxe1 7. Kf5 Qd2 8. Qe4+ Kf1 9. f4 Qd7+ —draw.

5b is derived from its published form:

White draws

Solution (Magyar Sakk´elet 1955, issue 8): 1. Bb8 Bg1 2. Be5 Bd4 3. Bd4: Kd4: 4. h6 Nf6 5. Kf6: a2 6. h7 a1Q 7. h8Q Ke5+ 8. Kg5: Qh8 —stalemate. If 6. – a1B 7. h8Q Ke4:+ 8. Kf7:! Bh8 9. Kg6 —draw. 1. – a2 2. Be5 Bg3: 3. Ba1 Bf2 4. h6 Bd4 5. Bd4: Kd4: 6. h7 a1Q 7. h8Q+ f6 8. Qe8: Ke4 9. Qg6+ and 10. Qf5 —draw. (1. h6? Nf6 2. Kf6: a2 3. Bd4 Kd4: 4. h7 a1Q 5. h8Q Ke4: 6. Kg5: Qe5+! —black wins.) Cook: (JM) 1 – Nf6! 2. Kxf6 a2 3. Be5 Bxg3 4. Ba1 Bf2! (4. – Be1? 5. h6 Bc3+ 6. Bxc3 Kxc3 7. h7 a1Q 8. h8Q Kd3+ 9. e5 Qf1+ 10. Ke7 Qf4 11. Qf6 Qxg4 12. Kxf7 Qh5+) 5. h6 Bd4+ 6.Bxd4 Kxd4 7. h7 Kxe4 (7. – a1Q 8. h8Q Kxe4+ 9. Kxg5 Qxh8—stalemate.) 8. Kxg5 a1B!! —Black wins. (8. – a1Q? 9. h8Q! Qxh8 —stalemate.) 36 GEORGE GRATZER¨

10. Cooks: 1. Ra4, Bd2 2. Rd4, Nc3 —checkmate 1. Ng5, Nxf6+ 2. Kf4 Qxe5 —checkmate Lucky for me, these were not discovered in the one hour Mr. Neukomm had to find cooks.

11. My #11 received the second prize in the Fourth Hungarian National Com- petition. The first prize winner was A. Kor´anyi’s endgame:

White wins

Solution (Magyar Sakk´elet 1957, issue 8/9, p. 139): 1. c6 Nb3 2. Bc5+ Nc5: 3. c7 Rb1+ 4. Ke2 Rb2+ 5. Kf1 Rb1+ 6. Kg2 Rb2+ 7. Kh3 Rb3+ 8. Kh4: g5+ 9. Kg4 Rb4+ 10. Kf5 Rf4+ 11. Kg6 Rf6+ 12. Kf6: Nd7+ 13. Ke6 Nb6 14. Bg4 Nc8 15. Kf6 Ne7 16. Kg5: Kg8 17. Bc6+ Kg7 18. Bc4 (b3) Nc8 19. Bb3 (c4) Ne7 20. Bc6 Kf8 21. Kf6 Ke8 22. Kg7 —white wins. SELECTED CHESS COMPOSITIONS 37

The final position is

an interesting .4 Of course, it is not this position that makes Kor´anyi’s work so remarkable, but the 22 interesting moves that lead up to it. It is difficult to use Fritz 11 or Hiarcs 12.1 MP to find a Cook in this composition. To look ahead 22 moves is a horizon too far. However, we can observe that in move 12. Kf6: reduces the number of pieces to 6:

so we can use the Knowledge4IT Website. Obviously, black moves Nf7+, and here is the surprise: 13. Ke6 wins in 19 moves and 13. Kf5 also wins in 19 moves. 13. Ke6 is the intended solution (see above); 13. Kf5 is a Cook: 13. – Nb6 14. Ke6 (14. Ke5 also wins.) Nc8 15. Ke5 Na7 16. Kd5 Nc8 17. Bg4 Ne7 18. Kd6 Kf7 19. Kd7 Kf6 20. Ke8 —white wins.

4A situation in a chess game in which a player is forced to make an undesirable or disadvan- tageous move. 38 GEORGE GRATZER¨

5. From the ashes. . . From the defective compositions of old, we are trying tyo resurrect some with J´anosMikitovics. 16. George Gr¨atzer& J´anosMikitovics MatPlus, May 2009

White wins

Solution: 1. Kb7!/i Ne8 2. a7!/ii Nc7 3. Nb3! Kd6/iii=main 4. Nc5!/iv Na8 5. Ne4+!/v Kd7 6. Ng5!!/vi 6...f5/vii=main 7. Nxe6 wins. i) 1. a7?? Kc8! 2. Nc2 Ne8 3. Nd4 Nc7#; 1. Kb8? Ne8! 2. a7 Nc7= ii) 2.Nb3? Nd6+= iii) main 3. ..Na8 4. Nc5+ Kd6 (4. ..Kd8 5. Ne4! f5 6. Ng5 Kd7 7. Nxe6+-) 5. Ne4+ (5. Na6? Kd7 6. Nb8+ Kd6 7. Nc6 f5! 8. Ne5 Nc7 9. Nc4+ Kd7 10. Ne5+ Kd6 11. Nc4+ Kd7 12. Ne5+ Kd6 positional draw.) 5. ..Kd7 6. Ng5+- main line; 3. ..e5 4. Nc5+ Kd8 5. Kc6+- (5. Na6? Na8 6. Nb8 f6! 7. Nc6+ Kd7=) iv) Thematic try 4. Nd4? Na8 (4. ..Kd7? 5. Nf3 f6 6. Nd2 f5 7. Nb3 e5 8. Nc5+ Kd8 9. Ne6+ Nxe6 10. a8Q++-; 4. ..e5 5. Nb5+ Nxb5) 5. Kxa8 (5. Nc6 f5 (5. ..f6 6. Nd4) 6. Ne5) 5. ..Kc7!= v) Thematic try 5. Na6? Kd7! 6. Nb8+ Kd6 7. Nc6 f5 8. Ne5 Nc7 (8. . f4? 9. Nc4+ Kd5 10. Kxa8+-) 9. Nf7+ (9. Ng6 Na8! (9 .. e5? 10. Ne7! f4 11. Nd5+-) 10. Nf4 e5 11. Nd5 e4=) 9 .. Kd7 10. Ng5 e5!= (10 .. Kd6? 11. Nxe6+-) ; 5. Na4? f5 6. Nb6 Nc7 7. Nc4+ Kd7 8. Ne5+ Kd6 (8 .. Kd8? 9. Nc6+ Kd7 10. Nd4 e5 11. Nxf5+-)9. Nc6 Na8 10. Nd8 f4= (10 .. Nc7? 11. Nxe6+-) vi) Thematic try 6. Nf6+?! Kd6! (6 .. Kd8? 7. Nh7!! e5 8. Nf6 Nc7 9. Ne8! Na8 10. Nd6! f6 11. Kc6!! (11. Ne4?! f5 12. Nd6 f4! (12 .. e4? 13. Nxf5+-) 13. Nf7+ Ke7!! (13 .. Kd7? 14. Nxe5++-) 14. Kxa8 f3=) 11 .. Nc7 12. Ne8! Na8 13. Nxf6!+-) 7. Ne8+ Kd7 8. Kxa8 Kc8 9. Nd6+ Kc7 10. Nxf7 Kc8 11. Ne5 Kc7 positional draw. vii) main 6 .. e5 7. Nxf7 a) 7. Ne4? f5= (7 .. Nc7? 8. Nf6+ Kd6 9. Ne8+ Nxe8 10. a8Q+-); b) 7. Nf3? f6 8. Nd2 f5 (8 .. Nc7? 9. Ne4 f5 10. Nc5+ Kd8 11. Ne6+ Nxe6 12. a8Q++-; 8 .. Kd8? 9. Ne4 f5 10. Nd6 f4 11. Nf7++-) 9. Nc4 e4 10. Nb6+ Kd6 11. Nxa8 e3 12. Nc7 e2 13. a8Q e1Q 14. Qa3+ (14. Qd8+ Kc5 15. Qd5+ Kb4 16. Qb5+ Ka3= (16 .. Kc3? 17. Qa5++-) ) 14 .. Kd7 (14 .. Ke5? 15. Qe7++-)15. Qa4+ Kd8=; 7 .. e4 8. Ne5++- (8. Ng5? e3=) K7/3k1ps1/P3p3/8/8/8/8/S7 Ka8 Sa1 Pa6 - Kd7 Sg7 Pe6 f7