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| (1) Posted by James Malcom [Tuesday, Jan 21, 2020 00:19]; edited by James Malcom [20-01-21] |
Record for the longest helpmate, in an illegal position?
This is a part two to a thread of mine a few months back: http://www.matplus.net/start.php?px=1579558217&app=forum&act=posts&fid=xshowm&tid=2326
I posted a h#59 awhile back, which had an illegal position that was was based on an illegal #45 (P0569739, originally a h#47) created by Otto Blathy. A few weeks ago, however, I came acrosss P0569740.
Karl Fabel, 1192 Schachmatt 01/08/1948
h#45 (orginally a h#48)
 (= 11+9 )
(As an aside, is the record for a dualed, but legal, helpmate? I think that a h#47 could be done if the g5 pawn was promoted into a bishop and placed on d4, upholding the original solution, minus one move)
This got my gears turning. Elongating Fable’s basic scheme to surpass my h#59 didn’t seem to be possbile. But then it occured to me yesterday. What if both of Blathy and Fable’s ideas could be combined to produce the motherload of helpmates, the longest ever in an illegal position?! Therefore I set to laboring away.
After some time, I found the motherload, finally surpassing my old h#59. I present my original monster before the world for all to see.
h#71
 (= 16+18 )
The first move is obvious: 1. Kh7 Bh3
I will leave it to you to solve it; I will not be suprised if it is cooked by a few moves.
Is this a record length for a helpmate in an illegal position using only normal pieces? Pawns are not not allowed on the 1st or 8th ranks of course, as those are not defined by the laws of chess, and are therefore fairy.
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| (2) Posted by Olaf Jenkner [Tuesday, Jan 21, 2020 00:40] |
It's a helpmate in 69 moves with billions of duals.
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| (3) Posted by James Malcom [Tuesday, Jan 21, 2020 00:52]; edited by James Malcom [20-01-21] |
Olaf, I have no cares for duals-the entire point is length, not uniqueness. Someone else can take up that challenge.
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| (4) Posted by Sarah Hornecker [Tuesday, Jan 21, 2020 01:10]; edited by Sarah Hornecker [20-01-21] |
Unless I miscounted: 63.K:g2 64.Kh1 65.g2 66.Bg3 67.Bh2 68.g1B Kf1 69.Bh4 Bg2 mate.
EDIT: Okay, I didn't count in the opper right corner bishops. So, how does this work in 69 moves? I get to 72 now, counting again (which means somewhere I miscounted by one also).
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| (5) Posted by James Malcom [Tuesday, Jan 21, 2020 02:10]; edited by James Malcom [20-01-21] |
The upper corner with the Black bishops is where I miscalucated for sure. After all, it is a very tight corridor that just barely allows for the king switch.
EDIT: I finally found a flaw in my endgame that reduces the total to 70 moves: 63. Ke1 Ka1!!! (This is the idea, to avoid the discovered check from the pawn move g2) 64, Kf1 65. Kb1 Kxg2 Kc1 66. Kh1Bh3 67. g2 Kd1 68. Be1 Kxe1 69. g1=B Kf1 70. Bh2 Bg2#
Olaf, where is the last move to be saved?
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| (6) Posted by Olaf Jenkner [Tuesday, Jan 21, 2020 17:23] |
1. Kh7 Bh3 10. Bf2 Bg4 11. Bxg1 Kxg1 12. Kg8 Bh3 13. Bh8 Bg4 14. Bfg7 Bh3 15. Kf8 Bg4 27. Kd2 Bg4 28. Ke1 Kh1 29. Kxf1 Bh3 30. Ke1 Bg4 31. Kd1 Kg1 32. Kc1 Kf1 33. Kb2 Ke1 34. Ka3 Kd1 35. Ka4 Kc1 36. Ka5 Kb1 37. Ka6 Ka2 38. Ka7 Kb3 39. Kb8 Ka4 40. Kc8 Kb5 41. Kd8 Ka6 42. Ke8 Kb7 43. Kf8 Kc8 44. Kg8 Kd7 45. Kh7 Ke8 46. Bf8 Kxf8 47. Bg7+ Kf7 48. Kh8 Kg6 49. Kg8 Bh3 50. Kf8 Kh7 51. Ke8 Kg6 52. Kd8 Kh7 53. Kc8 Kg6 54. Kb8 Kxg7 55. Ka7 Kf8 56. Kb6 Ke8 57. Ka5 Kd7 58. Kb4 Kc8 59. Ka3 Kb7 60. Kb2 Ka6 61. Kc1 Ka5 62. Kd2 Ka4 63. Ke1 Ka3 64. Kf2 Lg4 65. Kxg2 Ka2 66. Kf1 Kb1 67. g2 Kc1 68. g1=B Kd1 69. Bhf2 Bh3#
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| (7) Posted by Jakob Leck [Tuesday, Jan 21, 2020 19:10]; edited by Jakob Leck [20-01-21] |
Around 70 moves sounds like quite a feat, but for me the duals are a(n unacceptable) downside. And the position is soo ridiculously illegal (of course this can't be qualified, but you know what I mean). Maybe you should define what kinds of illegality you are willing to accept for record attempts. If you wouldn't mind adding material to the 34 (!) pieces I would suggest throwing in some black bishops to slow down the kings. I can't be bothered to analyze how many, but a black Ba7 would make it at least one move longer.
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| (8) Posted by James Malcom [Tuesday, Jan 21, 2020 21:47]; edited by James Malcom [20-01-22] |
To Olaf-Many thanks. That mating idea is only obvious once it is pointed out.
Jakob, I define illegality as being. able to place any amount of orthodox chess pieces in amounts or structures not possbile from the starting position. The only restriction is that pawns cannot be placed on the first and last ranks. Kings can in an illegal check so long so they can legally get out of it when the solution starts. Of course, both kings cannot be in check at the same, Drumare’s 1980 #5 Babson is a suitable example of my stance on illegality,
And as for placing more material, thanks for the idea. I have now extended it to it’s maximum. It has billions of duals of course.
h#??? ( It’s a h#103 at the most)
 (= 15+29 )
EDIT.: I this as a pzzle Puzzling Stack Exchange, and I have modified a user’s answer to have the known ending of Bh3#. This reduced my solution by 2 moves.
The best solution so far: 1... Kh7 2. Bh3 Kg8 3. Bg4 Bh8 4. Bh3 Bfg7 5. Bg4 Kf8 6. Bh3 Ke8 7. Bg4 Kd8 8. Bh3 Kc8 9. Bg4 Bg1 10. Kxg1 Bf2+ 11. Kh1 Bg1 12. Kxg1 Be1 13. Kh1 Bf2 14. Bh3 Bd2 15. Bg4 Bbc1 16. Bh3 Bde1 17. Bg4 Bcd2 18. Bh3 Bac1 19. Bg4 Bba3 20. Bh3 B5b4 21. Bg4 B6a5 22. Bh3 B7b6 23. Bg4 B8a7 24. Bh3 Bg1 25. Kxg1 Bf2+ 26. Kh1 Bg1 27. Bg4 Be1 28. Bh3 Bcd2 29. Kxg1 Bf2+ 30. Kh1 Bac1 31. Bg4 Bba3 32. Bh3 B5b4 33. Bg4 B6a5 34. Bh3 B7b6 35. Bg4 Bg1 36. Kxg1 Be1 37. Kh1 Bf2 38. Bh3 Bd2 39. Bg4 Bac1 40. Bh3 Bba3 41. Bg4 B5b4 42. Bh3 Kb8 43. Bg4 Ka7 44. Bh3 Ka6 45. Bg4 Ka5 46. Bh3 Ka4 47. Bg4 Bg1 48. Kxg1 Be1 49. Bh3 Bf2+ 50. Kh1 Bd2 51. Bg4 Bac1 52. Bh3 Bg1 53. Kxg1 Be1 54. Kh1 Bf2 55. Bg4 Bd2 56. Bh3 Ka3 57. Bg4 Kb2 58. Bh3 Kc1 59. Bg4 Kd1 60. Bh3 Ke1 61. Bg4 Kxf1 62. Bh3 Ke1 63. Bg4 Bg1 64. Kxg1 Kd1 65. Kf1 Be1 66. Bh3 Kc1 67. Kxe1 Kb2 68. Kd1 Ka3 69. Kc1 Ka4 70. Kb1 Ka5 71. Ka2 Ka6 72. Kb3 Ka7 73. Ka4 Kb8 74. Kb5 Kc8 75. Ka6 Kd8 76. Kb7 Ke8 77. Kc8 Kf8 78. Kd8 Kg8 79. Ke8 Bf8 80. Bg4 Kh7 81. Kxf8 Bg7+ 82. Kf7 Kh8 83. Kg6 Kg8 84. Bh3 Kf8 85. Bg4 Ke8 86. Bh3 Kd8 87. Kf7 Kc8 88. Ke8 Kb8 89. Kd8 Ka7 90. Kc8 Ka6 91. Bg4 Ka5 92. Kb7 Ka4 93. Ka6 Ka3 94. Kb5 Kb2 95. Ka4 Kc1 96. Kb3 Kd1 97. Ka2 Ke1 98. Kb1 Kf2 99. Ka2 Kxg2 100. Kxa1 Kf1 101. Kb1 g2 102. Kc1 g1=B 103. Kd1 Bhf2 104. Bh3#
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| (9) Posted by Jakob Leck [Tuesday, Jan 21, 2020 22:44]; edited by Jakob Leck [20-01-21] |
Well, I didn't play through it all because I don't have enough chess pieces and my chess software won't let me set up that much black material. But I figured that B3b2 on the 14th move must be a waste of time and also that the problem could be made longer by moving the black Bb8 to g1 (or even h2?). Then the long line of bishops has to back up into the corner to make it possible for the white king to capture the first of them before it can slowly move forward.
Edit: We both forgot to think about adding white bishops, that should yield some extra moves... ;)
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| (10) Posted by Olaf Jenkner [Wednesday, Jan 22, 2020 00:28]; edited by Olaf Jenkner [20-01-22] |
Gustav is made for chess. The data structure is designed for
maximum of 16 pieces per side. So it crashed in the initial
position of the h#71. After the 11th move there were only
17 black pieces left and Gustav did the job. Of course the
result might be wrong because of indefinite behavior but I
played the line and it was OK.
During the next days I'll try to extend the data structure
to make a test possible. At the moment I don't know of any
side effect because there are many things entwined. We'll
see in some days.
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| (11) Posted by James Malcom [Wednesday, Jan 22, 2020 03:24]; edited by James Malcom [20-01-22] |
To Jakob-I did try moving the b8 bishop to g1, but I found a solution in 95 moves, which probably means that will not surpass my current one. And adding more White bishops is a no-go because that leads to all sorts of cooks with Black being mated on the a8 square.
To Olaf-I appreciate the testing very much. You don't have to you know. I can most certainly wait a few days. Is it all feasible to find a shorter solution by "hand"? I use Apronus (https://www.apronus.com/chess/pgnviewer/) to play out my solutions electronically.
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| (12) Posted by Jakob Leck [Wednesday, Jan 22, 2020 19:30] |
You're right, my suggestions don't work.
For the position you posted above I have found a solution in 104 moves:
1... Kh7 2. Bh3 Bg1 3. Kxg1 Bf2+ 4. Kh1 Bde1 5. Bg4 Bcd2 6. Bh3 Bbc1 7. Bg4 Bg1
8. Kxg1 Bf2+ 9. Kh1 Bde1 10. Bh3 Bcd2 11. Bg4 Bac1 12. Bh3 Bba3 13. Bg4 B5b4 14.
Bh3 B6a5 15. Bg4 B7b6 16. Bh3 B8a7 17. Bg4 Bh8 18. Bh3 Bfg7 19. Bg4 Kg8 20. Bh3
Kf8 21. Bg4 Ke8 22. Bh3 Kd8 23. Bg4 Kc8 24. Bh3 Kb8 25. Bg4 Bg1 26. Kxg1 Bf2+
27. Kh1 Bg1 28. Kxg1 Be1 29. Bh3 Bf2+ 30. Kh1 Bg1 31. Kxg1 Bd2 32. Kh1 Be1 33.
Bg4 Bf2 34. Bh3 Bg1 35. Kxg1 Bc1 36. Kh1 Bd2 37. Bg4 Be1 38. Bh3 Bf2 39. Bg4 Bg1
40. Kxg1 Ba3 41. Kh1 B5b4 42. Kg1 Bc1 43. Kh1 B6a5 44. Kg1 B7b6 45. Kh1 Ka7 46.
Kg1 Ka6 47. Kh1 Bba3 48. Kg1 B5b4 49. Kh1 Ka5 50. Bh3 Bd2 51. Bg4 Be1 52. Bh3
Bf2 53. Bg4 Bg1 54. Kxg1 B3b2 55. Kh1 Ka4 56. Kg1 Ka3 57. Kh1 Ka2 58. Kg1 Kb1
59. Kh1 Kc1 60. Kg1 Kd1 61. Kh1 Ke1 62. Bh3 Kxf1 63. Bg4 Ke1 64. Kg1 Kd1 65. Kf1
Kc1 66. Ke1 Kb1 67. Kd1 Ka2 68. Bh3 Bc1 69. Kxc1 Ka3 70. Kb1 Ka4 71. Ka2 Ka5 72.
Kb3 Ka6 73. Ka4 Ka7 74. Kb5 Kb8 75. Ka6 Kc8 76. Bg4 Kd8 77. Kb7 Ke8 78. Kc8 Kf8
79. Kd8 Kg8 80. Ke8 Bf8 81. Bh3 Kh7 82. Kxf8 Bg7+ 83. Kf7 Kh8 84. Kg6 Kg8 85.
Bg4 Kf8 86. Bh3 Ke8 87. Kxg7 Kd8 88. Kf8 Kc8 89. Ke8 Kb8 90. Kd8 Ka7 91. Kc8 Ka6
92. Bg4 Ka5 93. Kb7 Ka4 94. Ka6 Ka3 95. Kb5 Kb2 96. Ka4 Kc1 97. Kb3 Kd1 98. Ka2
Ke1 99. Kxa1 Kf1 100. Ka2 Kxg2 101. Ka1 Kf1 102. Kb1 g2 103. Kc1 Bf2 104. Kd1
g1=B 105. Bh3#
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| (13) Posted by James Malcom [Wednesday, Jan 22, 2020 19:44]; edited by James Malcom [20-01-22] |
Jakob, I edited my post. The current solution is now 103 moves, one shorter than yours. I appreciate your efforts though. However, I am sure that you can find a shorter solution using that solution! :-)
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| (14) Posted by Jakob Leck [Wednesday, Jan 22, 2020 21:38] |
98 moves:
1... Kh7 2. Bh3 Kg8 3. Bg4 Bh8 4. Bh3 Bfg7 5. Bg4 Kf8 6. Bh3 Ke8 7. Bg4 Kd8 8.
Bh3 Kc8 9. Bg4 Bg1 10. Kxg1 Bf2+ 11. Kh1 Bg1 12. Kxg1 Be1 13. Kh1 Bf2 14. Bh3
Bd2 15. Bg4 Bbc1 16. Bh3 Bde1 17. Bg4 Bcd2 18. Bh3 Bac1 19. Bg4 Bba3 20. Bh3
B5b4 21. Bg4 B6a5 22. Bh3 B7b6 23. Bg4 B8a7 24. Bh3 Bg1 25. Kxg1 Bf2+ 26. Kh1
Bg1 27. Bg4 Be1 28. Bh3 Bcd2 29. Kxg1 Bf2+ 30. Kh1 Bac1 31. Bg4 Bba3 32. Bh3
B5b4 33. Bg4 Kb8 34. Bh3 Ka8 35. Bg4 Bb8 36. Bh3 Ka7 37. Bg4 Ka6 38. Bh3 Ka5 39.
Bg4 Bg1 40. Kxg1 Be1 41. Kh1 Bf2 42. Bh3 Bd2 43. Bg4 B3b2 44. Bh3 Ka4 45. Bg4
Ka3 46. Bh3 Ka2 47. Bg4 Kb1 48. Bh3 Kc1 49. Bg4 Kd1 50. Bh3 Ke1 51. Bg4 Kxf1 52.
Bh3 Ke1 53. Bg4 Bg1 54. Kxg1 Kd1 55. Bh3 Kc1 56. Kf1 Be1 57. Kxe1 Kb1 58. Kd1
Bc1 59. Bg4 Ka2 60. Kxc1 Ka3 61. Kb1 Ka4 62. Ka2 Ka5 63. Kb3 Ka6 64. Ka4 Ka7 65.
Kb5 Ka8 66. Ka6 B8a7 67. Bh3 Kb8 68. Bg4 Kc8 69. Bh3 Bb8 70. Bg4 Kd8 71. Kb7 Ke8
72. Kxb8 Kf8 73. Kc8 Kg8 74. Kd8 Bf8 75. Ke8 Kh7 76. Kxf8 Bg7+ 77. Kf7 Kh8 78.
Kg6 Kg8 79. Bh3 Kf8 80. Bg4 Ke8 81. Kxg7 Kd8 82. Kf8 Kc8 83. Ke8 Kb8 84. Kd8 Ka7
85. Kc8 Ka6 86. Bh3 Ka5 87. Kb7 Ka4 88. Ka6 Ka3 89. Kb5 Kb2 90. Ka4 Kc1 91. Kb3
Kd1 92. Ka2 Ke1 93. Bg4 Kf1 94. Kxa1 Kxg2 95. Ka2 Kf1 96. Kb1 g2 97. Kc1 Bf2 98.
Kd1 g1=B 99. Bh3#
Beat that!
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| (15) Posted by James Malcom [Thursday, Jan 23, 2020 02:45] |
Amazing work! I am not surprised that it went below the 100-move mark. I do think, however, that shortest solution will still be in the 90-move range. This will definitely ease the burden on Olaf's computer!
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| (16) Posted by Olaf Jenkner [Thursday, Jan 23, 2020 19:10] |
My computer will not find the shortest solution
unless it is a mate in 93.
I don't know why but it's getting slower. In many
cases one reason is full hash tables. At the moment only
23% of the room is used.
The search for a mate in 94 moves will take about a week.
74: 00 : 00 : 15 : 16 1.13
75: 00 : 00 : 17 : 25 1.14
76: 00 : 00 : 20 : 01 1.15
77: 00 : 00 : 23 : 11 1.16
78: 00 : 00 : 27 : 03 1.17
79: 00 : 00 : 31 : 47 1.18
80: 00 : 00 : 37 : 39 1.18
81: 00 : 00 : 44 : 59 1.19
82: 00 : 00 : 54 : 15 1.21
83: 00 : 01 : 06 : 13 1.22
84: 00 : 01 : 22 : 05 1.24
85: 00 : 01 : 44 : 51 1.28
86: 00 : 02 : 15 : 35 1.29
87: 00 : 03 : 01 : 06 1.34
88: 00 : 04 : 12 : 03 1.39
89: 00 : 06 : 12 : 02 1.48
90: 00 : 10 : 24 : 46 1.68
91: 00 : 18 : 38 : 25 1.79
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| (17) Posted by James Malcom [Friday, Jan 24, 2020 03:55] |
Well, as a compromise, if there is no solution in 93 moves found after testing, at least you will guaranteed that the optimum solution is between 93-98 moves, which would help further restraint on the numbers.
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| (18) Posted by Hauke Reddmann [Friday, Jan 24, 2020 17:09] |
Which is definitely an improvement over the problem
with Graham's number :-)
https://googology.wikia.org/wiki/Graham%27s_number
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| (19) Posted by Olaf Jenkner [Sunday, Jan 26, 2020 19:23]; edited by Olaf Jenkner [20-01-26] |
At my first attempt (see above) I used 4444 MB hashtables.
Now I used 11111 MB. At depth 91 it ran 4 times faster:
74: 00 : 00 : 14 : 29 . . 1.13
75: 00 : 00 : 16 : 25 . . 1.13
76: 00 : 00 : 18 : 46 . . 1.14
77: 00 : 00 : 21 : 34 . . 1.15
78: 00 : 00 : 24 : 55 . . 1.15
79: 00 : 00 : 28 : 53 . . 1.16
80: 00 : 00 : 33 : 25 . . 1.16
81: 00 : 00 : 38 : 46 . . 1.16
82: 00 : 00 : 45 : 07 . . 1.16
83: 00 : 00 : 52 : 40 . . 1.17
84: 00 : 01 : 01 : 38 . . 1.17
85: 00 : 01 : 12 : 19 . . 1.17
86: 00 : 01 : 24 : 56 . . 1.17
87: 00 : 01 : 39 : 53 . . 1.18
88: 00 : 01 : 57 : 49 . . 1.18
89: 00 : 02 : 21 : 55 . . 1.20
90: 00 : 03 : 00 : 22 . . 1.27
91: 00 : 04 : 34 : 24 . . 1.52
92: 00 : 13 : 33 : 02 . . 2.96
93: 02 : 14 : 56 : 49 . . 4.65
The slowdown is dramatically, 94 moves are far away.
The interesting thing is, that only 12% of the hash positions
are used. The reason might be hash collisions because the
stored positions are very similar. This behaviour I also noticed
in some long series movers. There is room for improvement
of the hash function.
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| (20) Posted by Olaf Jenkner [Monday, Jan 27, 2020 06:43]; edited by Olaf Jenkner [20-01-27] |
A new attempt with 13333 MB Hashtables was successful.
It is a helpmate in 97 moves:
1.Kg6-h7 Lg4-h3 2.Kh7-g8 Lh3-g4 3.Lf2-g1 Lg4-h3 4.Lg7-h8 Lh3-g4 5.Lf8-g7 Lg4-h3 6.Kg8-f8 Lh3-g4 7.Kf8-e8 Lg4-h3 8.Ke8-d8 Lh3-g4
9.Kd8-c8 Kh1xg1 10.Le1-f2 Kg1-h1 11.Ld2-e1 Lg4-h3 12.Lc1-d2 Lh3-g4 13.Lb2-c1 Lg4-h3 14.Lf2-g1 Lh3-g4 15.La3-b2 Lg4-h3 16.Lb4-a3 Lh3-g4
17.La5-b4 Lg4-h3 18.Lb6-a5 Lh3-g4 19.La7-b6 Lg4-h3 20.Lb8-a7 Lh3-g4 21.Kc8-b8 Lg4-h3 22.Kb8-a8 Lh3-g4 23.La7-b8 Lg4-h3 24.Ka8-a7 Lh3-g4
25.Ka7-a6 Lg4-h3 26.Lb6-a7 Lh3-g4 27.La5-b6 Lg4-h3 28.Ka6-a5 Lh3-g4 29.Ka5-a4 Lg4-h3 30.Lb4-a5 Lh3-g4 31.La3-b4 Lg4-h3 32.Ka4-a3 Lh3-g4
33.Ka3-a2 Lg4-h3 34.Ka2-b1 Kh1xg1 35.Le1-f2 Kg1-h1 36.Ld2-e1 Lh3-g4 37.Lc1-d2 Lg4-h3 38.Kb1-c1 Lh3-g4 39.Kc1-d1 Lg4-h3 40.Lf2-g1 Kh1xg1
41.Le1-f2 Kg1-h1 42.Kd1-e1 Lh3-g4 43.Ke1xf1 Lg4-h3 44.Kf1-e1 Lh3-g4 45.Ke1-d1 Lg4-h3 46.Kd1-c1 Lh3-g4 47.Kc1-b1 Lg4-h3 48.Kb1-a2 Lh3-g4
49.Lf2-g1 Kh1xg1 50.Ka2-a3 Kg1-f1 51.Ld2-e1 Kf1xe1 52.Ka3-a4 Ke1-d1 53.Lb2-c1 Kd1xc1 54.Lb4-a3 Kc1-d1 55.La3-c1 Lg4-h3 56.La5-b4 Lh3-g4
57.Ka4-a5 Lg4-h3 58.Ka5-a6 Lh3-g4 59.Lb6-a5 Lg4-h3 60.La7-b6 Lh3-g4 61.Ka6-a7 Lg4-h3 62.Ka7-a8 Kd1xc1 63.Lb4-a3 Kc1-b1 64.Lb8-a7 Kb1-a2
65.Ka8-b8 Ka2xa3 66.La5-b4 Ka3-a4 67.Kb8-c8 Ka4-b5 68.Kc8-d8 Kb5-a6 69.Kd8-e8 Ka6-b7 70.La7-b8 Kb7xb8 71.Ke8-f8 Kb8-c8 72.Kf8-g8 Kc8-d7
73.Kg8-h7 Kd7-e8 74.Lg7-f8 Ke8xf8 75.Lh8-g7 Kf8-f7 76.Kh7-h8 Kf7-g6 77.Kh8-g8 Lh3-g4 78.Kg8-f8 Kg6-h7 79.Kf8-e8 Kh7-g6 80.Ke8-d8 Kg6-h7
81.Kd8-c8 Kh7-g6 82.Kc8-b8 Kg6-h7 83.Kb8-a7 Kh7-g6 84.Ka7-a6 Kg6-f7 85.Ka6-a5 Kf7-e8 86.Ka5-a4 Ke8-d7 87.Ka4-a3 Kd7-c8 88.Ka3-b2 Kc8-b7
89.Kb2-c1 Kb7-a6 90.Kc1-d2 Ka6-b5 91.Kd2-e1 Kb5-a4 92.Ke1-f2 Ka4-b3 93.Kf2xg2 Kb3-a2 94.Kg2-f1 Ka2-b1 95.Bg3-g2 Kb1-c1 96.g2-g1L Kc1-d1 97.Lh4-f2 Lg4-h3#
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