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MatPlus.Net Forum General Most squares white's king must visit?

### Most squares white's king must visit?

What's the most different squares White's king visits in one solution-line of a directmate or win-study?

I know there are series-problems entailing long king-walks but that's not what I'm asking about here.

I appreciate the possibility that Black, by choice of move, can choose where to force White's king, but I'm more interested in how many different squares White's king must visit successively than in how many hypothetical alternatives there might be.

First, a study by Árpád Rusz posted in 2008 at https://www.chessproblem.net/viewtopic.php?f=12&t=192&p=358

Solution and annotations by Rusz.
(= 5+4 )

6b1/8/8/2n2k2/8/3PP3/1p3P2/1B1K4

1. d4+ Ne4 (1... Kg4 2. dxc5 +-) 2. f3 Bb3+ 3. Ke1 Bd5 4. Kf1 (4. fxe4+? Bxe4 =) Bc4+ 5. Kg2 Bd5 6. Kh3 Bb7 7. Kh4 Bc6 8. Kh5 Be8+ 9. Kh6 Bc6 10. Kg7 Bd5 11. Kf8 Bc6 (11... Kf6 12. fxe4 +-) 12. Ke7 and the white King will manage to capture the black Pawn.

visited 10 squares identified in Rusz's solution. can guard d7 and make visit at least 3 more to get to rank 6. then needs at least 4 more to reach b2, giving at least 17.

Next, if not from the sublime to the ridiculous, then at least from the beauty of the endgame study to the incomprehensibility of the tablebase. Here is a line of play from that KQRNvKQN position whose win is the longest. Annotations by Guy Haworth.
(= 4+3 )

7Q/N7/4K3/8/n5q1/8/5R2/2k5

1. Ke5! Qg3+' 2. Rf4! Qg5+' 3. Rf5! Qg3+' 4. Kf6' Qd6+' 5. Kf7' Qc7+' 6. Kg6' Qg3+' 7. Rg5' Qd3+' 8. Kf6' Qd6+' 9. Kf5' Qd3+' 10. Kf4' Qd2+' 11. Kg4' Qd1+' 12. Kg3' Qg1+' 13. Kf4! Qf2+' 14. Kg4! Qg2+' 15. Kf5' Qf3+' 16. Ke6' Qb3+' 17. Kf6' Qb6+' 18. Kf5! Qf2+' 19. Kg6' Qc2+' 20. Rf5' Qg2+' 21. Kf6' Qb2+' 22. Re5! Qf2+' 23. Ke6' Qb6+' 24. Kf7' Qb7+' 25. Kf8' Qb8+' 26. Re8! Qb4+' 27. Kf7' Qb3+' 28. Ke7' Qe3+' 29. Kd6' Qc5+' 30. Ke6! Qb6+' 31. Kf5' Qf2+' 32. Ke4' Qe1+' 33. Kd3' Qg3+' 34. Kc4' Nb2+' 35. Kd5! Qf3+' 36. Ke5' Qe3+' 37. Kf5' Qf2+' 38. Kg6' Qg1+' 39. Kh6' Qh1+' 40. Kg7' Qb7+' 41. Kg6' Qg2+' 42. Kf7' Qd5+' 43. Re6' Qd7+' 44. Re7! Qd5+' 45. Kg6' Qd3+' 46. Kg5' Qg3+' 47. Kf5! Qf2+' 48. Ke6' Qb6+' 49. Kf7' Qb3+' 50. Re6' Qb7+' 51. Kg6' Qg2+' 52. Kh7' Qh1+' 53. Rh6' Qe4+' 54. Kg7' Qd4+' 55. Kg6' Qd3+' 56. Kf6' Qd6+' 57. Kf5' Qd3+' 58. Ke6' Qa6+' 59. Ke5' Qa5+' 60. Ke4' Qe1+' 61. Kf5' Qf2+' 62. Ke5' Qe3+' 63. Kd5' Qf3+' 64. Kc5' Qa3+' 65. Kb5' Qa4+' 66. Kb6! Nc4+' 67. Kb7! Qb4+' 68. Kc7' Qc5+' 69. Nc6' Qb6+' 70. Kd7' Qb7+' 71. Kd8' Qa8+' 72. Kc7' Qxh8' {ending 71 consecutive 'spite' checks by the loser, a longer sequence than in KQRKQ} 73. Rxh8! {KRNKN: dtc/m/z = -13/-19/-13m}' Kc2' 74. Rd8' Kc3' 75. Kb7' Ne3' 76. Ne5' Nf5' 77. Rd3+' Kb4' 78. Rf3' Ne7' 79. Nc6+' Nxc6' 80. Kxc6' {KRK: dtx = -12m} Kc4' 81. Re3' Kd4' 82. Re6' Kc4' 83. Rd6' Kb4' 84. Rd4+' Kb3' 85. Kb5' Kc3' 86. Rd5' Kb3' 87. Rc5' Ka3' 88. Kc4' Kb2' 89. Kb4' Ka2' 90. Kc3' Ka1' 91. Kc2' Ka2% 92. Ra5#'

If I counted correctly, visited 30 squares. But no doubt there are White duals galore and White sometimes had the choice of getting out of check in some other way than moving to a square not visited before.

Henneberger Rabid Rook studies?

I did not count!

Thanks for the name-check, Hauke. (The web page turned out to be useless -- mostly irrelevant junk. Not your fault, Hauke, but Facebook's.) I wonder, is this the problem you were thinking of?

Moriz Henneberger
Basler Nachrichten, 1956, no. 4509
P1136319
(= 5+2 )

8/1BK5/7r/8/8/8/2RNR3/3k4
#22

That reminded me of a problem I found at http://www.chess.com/article/view/mate-in-4-or-more?page=2 (it's the 4th problem on that page). Annoyingly, although the web page's author gave credit for the previous three problems on that page, they didn't do likewise with this one.

(= 10+3 )

k7/1pP5/1P6/8/8/1K3rPR/1PPPPP2/8
#16

Henneberger #22 solution:

From Anton Baumann in PDB: 1.Se4 Th7+ 2.Kd6 Td7+ 3.Ke5 Td5+ 4.Kf4 Tf5+ 5.Ke3 Tf3+ 6.Kd4 Td3+ 7.Kc4 Td4+ 8.Kc3 Td3+ 9.Kb2 Tb3+ 10.Ka1 Tb1+ 11.Ka2 Ta1+ 12.Kb3 Ta3+ 13.Kc4 Ta4+ 14.Kc5 Ta5+ 15.Kc6 Ta6+ 16.Kc7 Tc6+ 17.Txc6 Kxe2 18.Tc3 Kf1! 19.Tc2 Ke1 20.La6 Kd1 21.Tc3,Tc5 Ke1 22.Tc1#

anon #16 solution:

1 e3 Rxe3+ 2 c3 Rxc3+ 3 Ka2 Ra3+ 4 Kb1 Ra1+ 5 Kc2 Rc1+ 6 Kd3 Rc3+ 7 Ke2 Re3+ 8 Kf1 Re1+ 9 Kg2 Rg1+ 10 Kf3 Rxg3+ 11 Ke2 Re3+ (Rxh3? 12 c8=Q#) 12 Kd1 Re1+ 13 Kc2 Rc1+ 14 Kb3 Rc3+ 15 Ka2 Ra3+ 16 Rxa3#

Last one is by Otto Gallischek: https://yacpdb.org/#302939

Tim Krabbé
Schaakbulletin 1976
(= 8+3 )

Win
1. Ne2 h1=Q+ 2. Bxh1 Ra1+ 3. Kc2 Rc1+ 4. Kd3 Rd1+ 5. Ke4 Rd4+ 6. Ke5 Rd5+ 7. Ke6 Rd6+ 8. Kf7 Rf6+ 9. Ke8 Rf8+ 10. Ke7 Re8+ 11. Kd6 Re6+ 12. Kc5 Re5+ 13. Kc4 Re4+ 14. Kc3 Rxe3+ 15. Kd4 Rd3+ 16. Kc5 Rd5+ 17. Kb4 Rb5+ 18. Kc4 Rb4+ 19. Kd3 Rd4+ 20. Kc2 Rd2+ 21. Kb1 Rb2+ 22. Kc1 Rb1+ 23. Kd2 Rd1+ 24. Ke3 Rd3+ 25. Kf2 Rxf3+ 26. Ke1 Rf1+ 27. Kd2 Rd1+ 28. Kc3 Rd3+ 29. Kc4 Rc3+ 30. Kd5 Rd3+ 31. Kc6 Rd6+ 32. Kb5 Rb6+ 33. Kc5 Rb5+ 34. Kd6 Rd5+ 35. Ke7 Re5+ 36. Kd7
24 squares

A.V. Alexeev
Lelo 1970
(= 10+8 )

Win
1. Qb1 Nc6+ 2. Rxc6 Ra8+ 3. Kxa8 Qb7+ 4. Kxb7 Rh7+ 5. Bg7 Rxg7+ 6. Rf7 Rxf7+ 7. Ne7 Rxe7+ 8. Bd7 Rxd7+ 9. Rc7 Rxc7+ 10. Ka8 Ra7+ 11. Kb8 Rb7+ 12. Kc8 Rc7+ 13. Kd8 Rd7+ 14. Ke8 Re7+ 15. Kf8 Rf7+ 16. Kg8 Rg7+ 17. Kh8 Rg8+ 18. Kh7 Rg7+ 19. Kh6 Rg6+ 20. Kh5 Rg5+ 21. Kh4 Rg4+ 22. Kh3 Rg3+ 23. Kh2 Rg2+ 24. Kh1 Rh2+ 25. Kg1 Rg2+ 26. Kf1 Rf2+ 27. Ke1 Re2+ 28. Kd1 Rd2+ 29. Kc1 Rd1+ 30. Kb2 Rd2+ 31. Ka1 Ra2+ 32. Qxa2
23 squares, including all corners

I. Chuiko
Shakhmatny v SSSR 1970
(= 12+5 )

Win (black to move)
1... Rf8+ 2. Kg7 Bh6+ 3. Kxh6 Rh5+ 4. Kxh5 Rf5+ 5. Ng5 Rxg5+ 6. Kh6 Rxg6+ 7. Kh5 Rg5+ 8. Kh4 Rg4+ 9. Kh3 Rg3+ 10. Kh2 Rh3+ 11. Kg2 Rg3+ 12. Kf1 Rf3+ 13. Ke2 Re3+ 14. Kd1 Rd3+ 15. Kc1 Rd1+ 16. Kb2 Rd2+ 17. Ka3 Ra2+ 18. Kb4 Ra4+ 19. Kb5 Ra5+ 20. Kc6 Rc5+ 21. Kd7 Rd5+ 22. Ke7 Re5+ 23. Kf7 Rf5+ 24. Kg7 Rg5+ 25. Bg6 Rxg6+ 26. Kh7 Rg7+ 27. Kh6 Rg6+ 28. Kh5 Rg5+ 29. Kh4 Rg4+ 30. Kh3 Rg3+ 31. Kh2 Rh3+ 32. Kg2 Rg3+ 33. Kf1 Rf3+ 34. Ke2 Re3+ 35. Kd1 Rd3+ 36. Kc1 Rd1+ 37. Kb2 Rd2+ 38. Ka3 Ra2+ 39. Kb4 Ra4+ 40. Kb5 Ra5+ 41. Kc6 Rc5+ 42. Kd7 Rd5+ 43. Nd6 Rxd6+ 44. Ke7 Re6+ 45. Kf7 Rf6+ 46. Kg7 Rg6+ 47. Kh7 Rg7+ 48. Kh6 Rg6+ 49. Kh5 Rg5+ 50. Kh4 Rg4+ 51. Kh3 Rg3+ 52. Kh2 Rh3+ 53. Kg2 Rg3+ 54. Kf1 Rf3+ 55. Ke2 Re3+ 56. Kd1 Rd3+ 57. Kc1 Rd1+ 58. Kb2 Rd2+ 59. Ka3 Ra2+ 60. Kb4 Ra4+ 61. Kb5 Ra5+ 62. Kc4 Rc5+ 63. Kd4 Rc4+ 64. Ke3 Rxc3+ 65. Kf4 Rf3+ 66. Kxf3

25 squares

Henneberger's composition that Hauke mentioned:
(= 7+2 )

Win (black to move)
Rg6+ 2. Ke7 Re6+ 3. Kd8 Re8+ 4. Kc7 Rc8+ 5. Kb6 Rc6+ 6. Kb5 Rc5+ 7. Kb4 Rc4+ 8. Kb3 Rc3+ 9. Ka2 Rxa3+ 10. Kb2 Ra2+ 11. Kb3 Rb2+ 12. Kc4 Rc2+ 13. Kd5 Rc5+ 14. Kd6 Rc6+ 15. Kd7 Rd6+ 16. Kc8 Rd8+ 17. Kc7 Rd7+ 18. Kb6 Rd6+ 19. Kb5 Rd5+ 20. Kb4 Rd4+ 21. Ka3 Rxa4+ 22. Kb3 Ra3+ 23. Kc4 Rc3+ 24. Kd5 Rc5+ 25. Kd6 Rc6+ 26. Kd7 Rd6+ 27. Kc8 Rd8+ 28. Kc7 Rd7+ 29. Kb6 Rd6+ 30. Kb5 Rd5+ 31. Ka4 Rxa5+ 32. Kb4 Ra4+ 33. Kc5 Rc4+ 34. Kd6 Rc6+ 35. Kd7 Rd6+ 36. Kc8 Rd8+ 37. Kc7 Rd7+ 38. Kb6 Rd6+ 39. Ka5 Rxa6+ 40. Kb5 Kxb7 41. Rh7+
But that's not many squares, just a lot of repetition.

Hi Rosie, nice to see you again.

I am pretty sure that I can give a definitive answer for both studies and directmates.

A while ago, I found a study in a Popov article on SuperProblem all about king routes. Google Translates will be your friend: http://superproblem.ru/archive/Stat/Stat50-1.html

Within is one study in which the king visits all corners in a round trip. I took the liberty to put it into PDB some time back: https://pdb.dieschwalbe.de/P1386031

Karen Sumbatyan & Oleg V. Pervakov, Shakhmaty v SSSR 1990, White Wins
(= 12+10 )

1. Bf4+ Kd5 2. Rc6 Rg1+ 3. Kxh2 R4g2+ 4. Kh3 Qd7+ 5. Nxd7 Rh2+ 6. Bxh2 Rg3+ 7. Kh4 Rg4+ 8. Kh5 Rg5+ 9. Kh6 Rg6+ 10. Kh7 Rg7+ 11. Kh8 Rh7+ 12. Kg8 Rg7+ 13. Kf8 Rxf7+ 14. Ke8 Re7+ 15. Kd8 Rxd7+ 16. Kc8 Rc7+ 17. Kb8 Rb7+ 18. Ka8 Rb8+ 19. Kxa7 Ra8+ 20. Kb6 Rb8+ 21. Kxa6 Ra8+ 22. Kb5 Rxa5+ 23. Kb4 Ra4+ 24. Kb3 Rb4+ 25. Ka2 Rb2+ 26. Ka1 Ra2+ 27. Kb1 Rb2+ 28. Kc1 Rb1+ 29. Kd2 Rd1+ 30. Kxe2 Rd2+ 31. Kf1 Rf2+ 32. Kg1 Rg2+ 33. Kh1 Rg1+ 34. Bxg1

29 squares are visited by the White king, including the one it starts on.

For directmates I have the current record of a 19 square journey. It was published in SuperProblem record book (http://superproblem.ru/archive/S_record-N.html): http://superproblem.ru/archive/probl/N/Malcom-20x-2020-1.gif See it in PDB as well: https://pdb.dieschwalbe.de/P1381360

(9) Posted by Rosie Fay [Wednesday, Jul 14, 2021 08:47]

Thank you, Joost and James, for your contributions. I find Sumbatyan and Pervakov's rambling-rook study impressive -- wK visits 29 different squares. It visits all four corners and doesn't capture in any of them.