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Knight Evasion Routes

By Andrei Kornilov, Moscow
Published in 'Die Schwalbe' Heft 181, Feb. 2000

For two horsemen it's difficult to get past each other on a narrow road. Similar difficulties are possible on the chess board too. A shows this in the form of retro-opposition of a white and a black knight. The action takes place in a corridor (a term coined by L. Ceriani) g1-h3-f2-d1-b2(-a4) with a sidestep h1. The solution can be easily visualized with a direct graph (comparable with the famous 15/16 puzzle from S. Loyd), in which only the squares reachable by the knights are present. It's obvious that the knight of the side which has a tempomove must make way for the other knight. Because e5-e6 results in an illegal retro-cage, the only tempomove that will release the position is d7-d6, while there's a white knight on f2 and a black one on h1.

In another scheme, the maneuver space of the knights is enlarged, see B (which uses 3 white rooks). C has a comparable scheme without promoted pieces, but with a shorter corridor. In D-H some variations to this scheme are shown. The rather immobile white knight in D allows, like a valve, the passage of the black knight. The white knight maneuvers in E allow the release of the white bishop. The corridor in F has a for white forbidden sidestep (d6). The shunting of the knights in G and H releases the white rook and the black bishop.

A similar expansion possibility of the theme is to increase the number of pieces that take place in the retro-maneuver. For instance, as I shows, the duo from A can be transformed into a trio easily. Long corridors are shown in the prizewinning J and its improvement(!) K. Other versions of this scheme are shown in L and M.

N improves this even further to a knight-quartet. The extra (promoted) knight is useful, because it actively takes part in the play (compare with B). Unfortunately the third knight plays only a minor role in the evasion mechanism. The route graph of O isn't sufficient for solving, because the unpromotion of the white knight can't be understood with it.

The next goal is a retro problem in which three knights of one side, and one of the other have to get past each other.

 

A L. Ceriani B L. Garaza
Fairy Chess Review 1957 Problem 1959
[N7/5p2/3pPP2/1PPk1KP1/1pR1pRrB/2pb1ppn/2PPP3/7N](solution) [8/3p2p1/2pP4/P1P2KPk/rBRqPRR1/p1prppp1/P1NP4/1N2n3]
#1 (14+11) #1 (14+13)
[routegraph A] [routegraph B]
C A. Kornilov D A. Kornilov
Redkije shanry plus 1995 Redkije shanry plus 1996
[5N2/4P1np/1PPPRP2/BrrQpp2/1pp2k1P/p2p2pK/3P2PR/7n](solution) [7B/6p1/2p1PPP1/1PP1RqRK/1prkBQrb/2pPpppn/1P6/2N5]
#1 (14+13) #1 (14+13)
[routegraph C] [routegraph D]
E A. Kornilov F A. Kornilov
Original Original
[4N3/2n2B1p/1PPPPP1P/1PBRrQnk/1p1ppKpb/2p2p2/5P2/8](solution) [4N3/1N4p1/1PP1PPpP/nPRbrkQ1/1ppKp1pn/4P2B/6P1/8](solution)
Release the position (14+12) Release the position (14+11)
[routegraph E] [routegraph F]
G A. Kornilov H A. Kornilov
Original Original
[5N2/4p2n/1PPPRPp1/1PQBrqP1/1ppKpkp1/5p1R/5P1B/6n1](solution) [8/4P2N/1PPPRP2/1PrbRrPn/1ppKpkp1/5pp1/3p3b/8](solution)
Release the position (14+12) Who wins? (11+13)
[routegraph G] [routegraph H]
I A. Kornilov J A. Kornilov
Original (after Ceriani) 1st prize, Ceriani-memorial, Die Schwalbe 1996
[8/5p2/3pPP2/1PPk1KP1/1pR1pRrB/2pb1ppn/1NPPP3/3N4](solution) [8/2NN3n/1PPPPPP1/BRRQprr1/1pp2kpK/3p3B/3P1pP1/8](solution)
#1 (14+11) #1 (16+10)
[routegraph I] [routegraph J]
K A. Kornilov L A. Kornilov
Die Schwalbe 1997 Europe Echecs 1997
[4N3/3N3n/1PPPPPP1/BpRQprr1/1pp2kpK/3p3B/3P2P1/8](solution) [5n2/2N1pPN1/1PPPrRp1/BrRppBP1/1p3kPK/p1p4p/3PP3/8](solution)
#1 (15+10) #1? (15+12)
[routegraph K] [routegraph L]
M A. Kornilov N A. Kornilov
Original diagrammes 1996
[5N1n/4ppNn/1PPPrrp1/1PBbRqp1/1ppKpkP1/4P3/5P2/4b3](solution) [4Nn2/3n3n/1PPkPPp1/BrbprRP1/Pp1ppKp1/6p1/3P4/8](solution)
Release the position (12+15) Release the position (11+14)
[routegraph M] [routegraph N]
O A. Kornilov
Original
[5N2/4p1Nn/1PPPRPp1/brRpBqrN/1p2kp1K/2p2Pp1/4P3/8](solution)
Release the position (13+13)
[routegraph O]

Solutions

A: 1. Nb6#?. The retroplay is: -1. Nf2-h1 Ng1-h3 -2. Nd1-f2 Nh3-g1 -3. Nb2-d1 Nf2-h3 -4. Nd1-b2 Nh1-f2 -5. Nf2-d1 d7-d6 -6. Nh3-f2 Nf2-h1 and further: Na1-f2; a5-a1=N; a4xb5, etc. So black has the move. 1. .. Rf4#!

B: 1. .. g6#?. The retroplay is: -1. .. Ng2-e1 -2. Na1-c2 Ne1-g2 -3. Nb3-a1 Nc2-e1 -4. Nc1-b3 Na1-c2 -5. Ne2-c1 Nb3-a1 -6. Ng1-e2 Nc1-b3 -7. Nh3-g1 Ne2-c1 -8. Nf2-h3 Ng1-e2 -9. Nd1-f2 Nh3-g1 -10. Nb2-d1 Nf2-h3 -11. Nd1-b2 Nh1-f2 -12. Nf2-d1 c7-c6 -13. Nh3-f2 and further: Ne5-h3; Qd5-d4 and the position unlocks. So white has the move. 1. Rh4#!

C: 1. Qf3#?. The retroplay is: -1. Nd7-f8 Ne8-g7 -2. Nb8-d7 Nc7-e8 -3. Na6-b8 Na8-c7 -4. Nc7-a6 a4-a3 -5. Ne8-c7 and further Ne4-a8, Qd4-d5 etc. So black has the move. 1. .. Nf2#!

D: 1. Nb3#?. The retroplay is: -1. Na2-c1 Ng1-h3 -2. Nc1-a2 Ne2-g1 -3. Na2-c1 Nc1-e2 -4. h7-h8=B! Nb3-c1 -5. Nc1-a2 Na1-b3 -6. Na2-c1 c7-c6 -7. Nc1-a2 a2-a1=N -8. h6-h7 a3-a2 -9. Na2-c1 and the position unlocks. So black has the move. 1. .. Nf4#!

E: The retroplay is: -1. Bg8-f7 Na8-c7! (-1. .. Na6-c7?) -2. Nc7-e8 c4-c3 -3. Na6-c7 Nc7-a8 -4. Nb8-a6 ~ -5. Nd7-b8 ~ -6. Nf8-d7 ~ -7. Ng6-f8 ~ -8. Bf7-g8 ~ -9. Be8-f7 ~ -10. Bd7-f8 ~ -11. Nh8-g6 ~ -12. Nf7-h8 ~ -13. Nd8-f7 ~ -14. Nb7-d8 ~ -15. Na5-b7 ~ -16. Nb3-a5 ~ -17. Nc1-b3 ~ -18. Ne2-c1 ~ -19. Ng1-e2 ~ -20. Nh3-g1 Nf7-g5 -21. Ng5-h3 Nd8-f7 -22. ~ Nb7-d8 -23. ~ Na5-b7 -24. ~ Nb3-a5 -25. ~ Na1-b3 -26. ~ a2-a1=N -27. ~ a3-a2 -28. ~ a4-a3 -29. ~ a5-a4 -30. a4xQb5 and the position unlocks.

F: The retroplay is: -1. Qh5xQg5 f7xRg6! (-1. h7xQg6? and the white knight can't get to g5) -2. Nd8-b7 Nb7-a5 -3. Nc7-e8 Nd6-b7 -4. Nb7-e8 ~ -5. Na5-b7 ~ -6. Na6-c7 ~ -7. Nb8-a6 ~ -8. Nd7-b8 ~ -9. Nf8-d7 ~ -10. Nb3-a5 ~ -11. Nc1-b3 ~ -12. Ne2-c1 ~ -13. Nh7-f8 Qf4-g5 -14. Ng5-h7 Qf1-f4 -15. Nc3-e2 Qa1-f1 -16. Ne2-c3 a2-a1 -17. ~ a3-a2 -18. ~ a4-a3 -19. ~ a5-a4 -20. a4xQb5 and the position unlocks.

G: The retroplay is: -1. Rg3-h3 Nh3-g1 -2. Nd7-f8 Nf8-h7 -3. Nb8-d7 Nd7-f8 -4. Na6-b8 Nb8-d7 -5. Nc7-a6 Na6-b8 -6. Na8-c7 Nc7-a6 -7. Bg1-h2 Ne8-c7 -8. Rg2-g3 Ng7-e8 -9. Rh2-g2 Nh5-g7 -10. Rh1-h2 Ng3-h5 -11. Bh2-g1 Ng1-h3 -12. Nc7-a8 Nh3-g1 -13. Ra1-h1 Ng1-h3 -14. Ra8-a1 Nh3-g1 -15. Rh8-a8 Ng1-h3 -16. h7-h8=R Nh3-g1 -17. h6-h7 Ng1-h3 -18. h5-h6 Ng3-g1 -19. h4-h5 h5xNg4 and the position unlocks.

H: 1. Re4 Be4 2. Re4#?. The retroplay is: -1. Nf8-h7 Ng7-h5 -2. Nd7-f8 Ne8-g7 -3. Nb8-d7 Nc7-e8 -4. Na6-b8 Na8-c7 -5. Nc7-a6 d3-d2 -6. Ne8-c7 Nc7-a8 -7. ~ Na6-c7 -8. ~ Nb8-a6 -9. ~ Nd7-b8 -10. ~ Nf8-d7 -11. ~ Ng6-f8 -12. ~ Nh4-g6 -13. ~ Ng2-h4 -14. ~ Ne3-g2 -15. ~ Bg1-h2 -16 ~ Bf2-g1 -17. ~ Be1-f2 -18. ~ Bd2-e1 -19. ~ Bc1-d2 -20. ~ Nd1-e3 -21. ~ Nc3-d1 -22. ~ Bb2-c1 -23. ~ Ba1-b2 -24. ~ a2-a1=B -25. ~ a3-a2 -26. ~ a4-a3 -27. ~ a5-a4 -28. a4xQb5 and the position unlocks. So black has the move. 1. .. Bg1#!

I: 1. Ne3#?. The retroplay is: -1. Nf2-d1 Ng1-h3 -2. Nh1-f2 Nh3-g1 -3. Na4-b2 Nf2-h3 -4. Nb2-a4 Nd1-f2 -5. Na4-b2 Nb2-d1 -6. Nf2-h1 Nd1-b2 -7. Nh3-f2 Nf2-d1 -8. Ng1-h3 Nh3-f2 -9. Nb2-a4 Nf2-h3 -10. Nd1-b2 Nh3-f2 -11. Nf2-d1 d7-d6 -12. Nh1-f2 Nf2-h3 etc. So black has the move. 1. .. Rf4#!

J: 1. g3#?. The retroplay is: -1. Na8-c7 Nf8-h7 -2. Nb8-d7 Nd7-f8 -3. Na6-b8 Nb8-d7 -4. Nc7-a6 Na6-b8 -5. Ne8-c7 Nc7-a6 -6. Ng7-e8 Ne8-c7 -7. Nc7-a8 f3-f2 -8. Na6-c7 Nc7-e8 -9. Nb8-a6 Na6-c7 -10. Nd7-b8 Nb8-a6 -11. Ne8-g7 Na6-b8 -12. Nc7-e8 Nb8-a6 -13. Na8-c7 Na6-b8 -14. Nb8-d7 Nc7-a6 -15. ~ Ne8-c7 -16. ~ Ng7-e8 -17. ~ Nh5-g7 -18. ~ Ng3-h5 -19. ~ Ne4-g3 Qd4-d5. So black has the move. 1. .. Rh5#!

K: 1. g3#?. The retroplay is: -1. Ng7-e8 Nf8-h7 -2. Nb8-d7 Nd7-f8 -3. Na6-b8 Nb8-d7 -4. Nc7-a6 Na6-b8 -5. Na8-c7 Nc7-a6 -6. Ne8-g7 a6xRb5 -7. Ng7-e8 Ne8-c7 -8. Nc7-a8 a7-a6 -9. Na6-c7 Nc7-e8 -10. Nb8-a6 Na6-c7 -11. Nd7-b8 Nb8-a6 -12. Ne8-g7 Na6-b8 -13. Nc7-e8 Nb8-a6 -14. Na8-c7 Na6-b8 -15. ~ Nc7-a6 -16. ~ Ne8-c7 -17. ~ Ng7-e8 -18. ~ Nh5-g7 -19. ~ Ng3-h5 -20. ~ Ne4-g3 -21. Qd4-d5. So black has the move. 1. Rh5#!

L: 1. Nd5#?. The retroplay is: -1. Na8-c7 Nd7-f8 -2. Ne8-g7 Nb8-d7 -3. Ng7-e8 Na6-b8 -4. Ne8-g7 Nc7-a6 -5. Ng7-e8 Ne8-c7 -6. Nc7-a8 a4-a3 -7. Na6-c7 Nc7-e8 -8. Nb8-a6 Na6-c7 -9. Nd7-b8 Nb8-a6 -10. Ne8-g7 Na6-b8 -11. Nc7-e8 Nb8-a6 -12. Na8-c7 Na6-b8 -13. Nb8-d7 Nc7-a6 -14. Na6-b8 Ne8-c7 -15. Nb8-a6 Ng7-e8 -16. Na6-b8 Nh5-g7 -16. Nb8-a6 Ng3-h5 -17. Na6-b8 Ne4-g3 -18. Rc4-c5. So no legal mate in 1 is possible.

M: The retroplay is: -1. e2-e3 Nd2-e1 -2. Nd7-f8 Nf8-h7 -3. Nb8-d7 Nd7-f8 -4. Na6-b8 Nb8-d7 -5. Nc7-a6 Na6-b8 -6. Na8-c7 Nc7-a6 -7. Ne8-g7 Bc1-d2 -8. Ng7-e8 Ne8-c7 -9. Nc7-a8 Ba3-c1 -10. Na6-c7 Nc7-e8 -11. Nb8-a6 Na8-c7 -12. Ne8-g7 ~ -13. Nc7-e8 ~ -14. Na6-c7 Nc7-a8 -15. ~ Ne8-c7 -16. ~ Ng7-e8 -17. ~ Nh5-g7 -18. ~ Ng3-h5 -19. ~ Nf1-g3 -20. ~ Ne3-f1 -21. ~ Nd1-e3 -22. ~ Nc3-d1 -23. ~ Bb2-~ -24. ~ Ba1-b2 -25. ~ a2-a1=B -26. ~ a3-a2 -27. ~ a4-a3 -28. ~ a5-a4 -29. ~ a6-a5 -30. a5xBb6 and the position unlocks.

N: The retroplay is: -1. Nc7-e8! (1. Ng7-e8?) Nb8-d7 -2. Na8-c7 Na6-b8 -3. Nc7-a8 Nd7-f8 -4. Na8-c7 Nc7-a6 -5. a4-a3 Ne8-c7 -6. Nc7-a8 Ng7-e8 -7. Na8-c7 Nb8-d7 -8. Nc7-a8 Na6-b8 -9. Na8-c7 Nc7-a6 -10. a2-a3 Ne8-c7 -11. Nc7-a8 Nf8-h7 -12. Na6-c7 Nc7-e8 -13. Nb8-a6 Ne8-g7 -14. Nd7-b8 Nh7-f8 -15. Nf8-d7 g7-g6 -16. Ng6-f8 Nf8-h7 -17. Nh8-g6 ~ -18. h7-h8=N ~ -19. h6-h7 ~ -20. h5-h6 ~ -21. h4-h5 h5xBg4 and the position unlocks.

O: The retroplay is: -1. f2-f3 g4-g3 -2. Nd7-f8 Nf8-h7 -3. Nb8-d7 Nd7-f8 -4. Na6-b8 Nb8-d7 -5. Nc7-a6 Na6-b8 -6. Na8-c7 Nc7-a6 -7. a7-a8=N! Na6-c7 -8. Ne8-g7 Nb8-a6 -9. Nc7-e8 Na6-b8 -10. Na8-c7 Nc7-a6 -11. Ng7-h5 Ne8-c7 -12. Nh5-g7 Ng7-e8 -13. Nc7-a8 Ne8-g7 -14. Na6-c7 Nc7-e8 -15. Nb8-a6 Na6-c7 -16. Nd7-b8 Nb8-a6 -17. Ng7-h5 Na6-b8 -18. Ne8-g7 Nb8-a6 -19. Nc7-e8 Na6-b8 -20. Na8-c7 Nc7-a6 -21. Nb8-d7 Ne8-c7 -22. ~ Ng7-e8 -23. ~ Nh5-g7 -24. ~ Ng3-h5 -25. ~ Nf1-g3 -26. ~ Nd2-f1 -27. ~ Nb3-d2 -28. ~ Nd4-b3 -29. Rc4-c5 and the position unlocks.