Huge work... But it will be done certainly!

[Hobacle]

2b1qrk1/4p3/3pPp1p/1pnP2p1/2p1P3/2P4P/2P1Q1PK/1B2BR2

The full pgn file of the #226:
[pgn][Event ""]
[Site ""]
[Date "2022.02.06"]
[Round ""]
[White ""]
[Black ""]
[Result "1-0"]
[FEN "1N2Q3/p6n/p5n1/p1p2rpb/p4k1r/K1P4p/2PP4/6B1 w - - 0 1"]
[SetUp "1"]

1. Bh2+ Kf3 2. Qe3+ Kg2 3. Qg1+ Kf3 4. Qf1+ Kg4 5. Qe2+ Rf3 6. Qe6+ Rf5 7. Nd7
Kf3 8. Qe3+ Kg2 9. Qg1+ Kf3 10. Qf1+ Kg4 11. Qe2+ Rf3 12. Qe6+ Rf5 13. Kb2 Kf3
14. Qe3+ Kg2 15. Qg1+ Kf3 16. Qf1+ Kg4 17. Qe2+ Rf3 18. Qe6+ Rf5 19. Kc1 Kf3
20. Qe3+ Kg2 21. Qg1+ Kf3 22. Qf1+ Kg4 23. Qe2+ Rf3 24. Qe6+ Rf5 25. Kd1 a3 26.
Kc1 Kf3 27. Qe3+ Kg2 28. Qg1+ Kf3 29. Qf1+ Kg4 30. Qe2+ Rf3 31. Qe6+ Rf5 32.
Kb1 Kf3 33. Qe3+ Kg2 34. Qg1+ Kf3 35. Qf1+ Kg4 36. Qe2+ Rf3 37. Qe6+ Rf5 38.
Ka2 Kf3 39. Qe3+ Kg2 40. Qg1+ Kf3 41. Qf1+ Kg4 42. Qe2+ Rf3 43. Qe6+ Rf5 44.
Kxa3 Kf3 45. Qe3+ Kg2 46. Qg1+ Kf3 47. Qf1+ Kg4 48. Qe2+ Rf3 49. Qe6+ Rf5 50.
Kb2 Kf3 51. Qe3+ Kg2 52. Qg1+ Kf3 53. Qf1+ Kg4 54. Qe2+ Rf3 55. Qe6+ Rf5 56.
Kc1 Kf3 57. Qe3+ Kg2 58. Qg1+ Kf3 59. Qf1+ Kg4 60. Qe2+ Rf3 61. Qe6+ Rf5 62.
Kd1 a4 63. Kc1 Kf3 64. Qe3+ Kg2 65. Qg1+ Kf3 66. Qf1+ Kg4 67. Qe2+ Rf3 68. Qe6+
Rf5 69. Kd1 a5 70. Kc1 Kf3 71. Qe3+ Kg2 72. Qg1+ Kf3 73. Qf1+ Kg4 74. Qe2+ Rf3
75. Qe6+ Rf5 76. Kd1 a6 77. Kc1 Kf3 78. Qe3+ Kg2 79. Qg1+ Kf3 80. Qf1+ Kg4 81.
Qe2+ Rf3 82. Qe6+ Rf5 83. Kd1 a3 84. Kc1 Kf3 85. Qe3+ Kg2 86. Qg1+ Kf3 87. Qf1+
Kg4 88. Qe2+ Rf3 89. Qe6+ Rf5 90. Kb1 Kf3 91. Qe3+ Kg2 92. Qg1+ Kf3 93. Qf1+
Kg4 94. Qe2+ Rf3 95. Qe6+ Rf5 96. Ka2 Kf3 97. Qe3+ Kg2 98. Qg1+ Kf3 99. Qf1+
Kg4 100. Qe2+ Rf3 101. Qe6+ Rf5 102. Kxa3 Kf3 103. Qe3+ Kg2 104. Qg1+ Kf3 105.
Qf1+ Kg4 106. Qe2+ Rf3 107. Qe6+ Rf5 108. Kb2 Kf3 109. Qe3+ Kg2 110. Qg1+ Kf3
111. Qf1+ Kg4 112. Qe2+ Rf3 113. Qe6+ Rf5 114. Kc1 Kf3 115. Qe3+ Kg2 116. Qg1+
Kf3 117. Qf1+ Kg4 118. Qe2+ Rf3 119. Qe6+ Rf5 120. Kd1 a4 121. Kc1 Kf3 122.
Qe3+ Kg2 123. Qg1+ Kf3 124. Qf1+ Kg4 125. Qe2+ Rf3 126. Qe6+ Rf5 127. Kd1 a5
128. Kc1 Kf3 129. Qe3+ Kg4 130. Qg1+ Kf3 131. Qf1+ Kg4 132. Qe2+ Rf3 133. Qe6+
Rf5 134. Kd1 a3 135. Kc1 Kf3 136. Qe3+ Kg2 137. Qg1+ Kf3 138. Qf1+ Kg4 139.
Qe2+ Rf3 140. Qe6+ Rf5 141. Kb1 Kf3 142. Qe3+ Kg2 143. Qg1+ Kf3 144. Qf1+ Kg4
145. Qe2+ Rf3 146. Qe6+ Rf5 147. Ka2 Kf3 148. Qe3+ Kg2 149. Qg1+ Kf3 150. Qf1+
Kg4 151. Qe2+ Rf3 152. Qe6+ Rf5 153. Kxa3 Kf3 154. Qe3+ Kg2 155. Qg1+ Kf3 156.
Qf1+ Kg4 157. Qe2+ Rf3 158. Qe6+ Rf5 159. Kb2 Kf3 160. Qe3+ Kg2 161. Qg1+ Kf3
162. Qf1+ Kg4 163. Qe2+ Rf3 164. Qe6+ Rf5 165. Kc1 Kf3 166. Qe3+ Kg2 167. Qg1+
Kf3 168. Qf1+ Kg4 169. Qe2+ Rf3 170. Qe6+ Rf5 171. Kd1 a4 172. Kc1 Kf3 173.
Qe3+ Kg2 174. Qg1+ Kf3 175. Qf1+ Kg4 176. Qe2+ Rf3 177. Qe6+ Rf5 178. Kd1 c4
179. Kc1 Kf3 180. Qe3+ Kg2 181. Qg1+ Kf3 182. Qf1+ Kg4 183. Qe2+ Rf3 184. Qe6+
Rf5 185. Kd1 a3 186. Kc1 Kf3 187. Qe3+ Kg2 188. Qg1+ Kf3 189. Qf1+ Kg4 190.
Qe2+ Rf3 191. Qe6+ Rf5 192. Kb1 Kf3 193. Qe3+ Kg2 194. Qg1+ Kf3 195. Qf1+ Kg4
196. Qe2+ Rf3 197. Qe6+ Rf5 198. Ka2 Kf3 199. Qe3+ Kg2 200. Qg1+ Kf3 201. Qf1+
Kg4 202. Qe2+ Rf3 203. Qe6+ Rf5 204. Kxa3 Kf3 205. Qe3+ Kg2 206. Qg1+ Kf3 207.
Qf1+ Kg4 208. Qe2+ Rf3 209. Qe6+ Rf5 210. Kb2 Kf3 211. Qe3+ Kg2 212. Qg1+ Kf3
213. Qf1+ Ke4 214. Qxc4+ Kf3 215. Qf1+ Kg4 216. Qe2+ Rf3 217. Qe6+ Rf5 218. Kc1
Kf3 219. Qe3+ Kg2 220. Qg1+ Kf3 221. Qf1+ Kg4 222. Qe2+ Rf3 223. Qe6+ Rf5 224.
Kd1 Nhf8 225. Nf6+ Kf3 226. Qe2# 1-0
[/pgn]

To finally prove this famous mate-in-226 composition has a shorter solution, we must simplify the work. Anyhow I've found a way to reduce the computation. Now we just need to find the direct DTM of these 17 positions.

Code: Select all

1. 8/3N3n/K3Q1n1/2p2rpb/2PP2kr/2P4p/7B/8 b - - 0 1

The following positions are similar.

2. 8/K2N3n/6n1/2p2rpb/2P1k2r/2P4p/3P3B/5Q2 w - - 0 1
3. 8/3N3n/K5n1/2p2rpb/2P1k2r/2P4p/3P3B/5Q2 w - - 0 1
4. 8/p2N3n/K5n1/2p2rpb/2P1k2r/2P4p/3P3B/5Q2 w - - 0 1
5. 8/3N3n/p5n1/K1p2rpb/2P1k2r/2P4p/3P3B/5Q2 w - - 0 1
6. 8/p2N3n/6n1/K1p2rpb/2P1k2r/2P4p/3P3B/5Q2 w - - 0 1
7. 8/p2N3n/p5n1/K1p2rpb/2P1k2r/2P4p/3P3B/5Q2 w - - 0 1
8. 8/3N3n/p5n1/p1p2rpb/K1P1k2r/2P4p/3P3B/5Q2 w - - 0 1
9. 8/p2N3n/6n1/p1p2rpb/K1P1k2r/2P4p/3P3B/5Q2 w - - 0 1
10. 8/p2N3n/p5n1/2p2rpb/K1P1k2r/2P4p/3P3B/5Q2 w - - 0 1
11. 8/p2N3n/p5n1/p1p2rpb/K1P1k2r/2P4p/3P3B/5Q2 w - - 0 1
12. 8/p2N3n/6n1/p1p2rpb/p1P1k2r/K1P4p/3P3B/5Q2 w - - 0 1
13. 8/p2N3n/p5n1/2p2rpb/p1P1k2r/K1P4p/3P3B/5Q2 w - - 0 1
14. 8/p2N3n/p5n1/p1p2rpb/2P1k2r/K1P4p/3P3B/5Q2 w - - 0 1
15. 8/p2N3n/p5n1/2p2rpb/p1P1k2r/p1P4p/K2P3B/5Q2 w - - 0 1
16. 8/p2N3n/p5n1/p1p2rpb/2P1k2r/p1P4p/K2P3B/5Q2 w - - 0 1
17. 8/p2N3n/p5n1/p1p2rpb/p1P1k2r/2P4p/1K1P3B/5Q2 w - - 0 1

But it's still too hard for my hardware. So I need aid.
Thank you for any help you can offer.

[peter]

Thank you for any help you can offer.

forum3/viewtopic.php?p=920369#p920369

You're welcome

[Hobacle]

Thank you for any help you can offer.

forum3/viewtopic.php?p=920369#p920369

You're welcome

Oh no... I pasted the link wrongly... Thanks for the right link...

[peter]

Thank you for any help you can offer.

forum3/viewtopic.php?p=920369#p920369

You're welcome

Oh no... I pasted the link wrongly... Thanks for the right link...

Welcome again

And one more help:
Take the position next to the one you want the DTM to prove for, try to figure out the Chest- params best to solve this one, then chance the setting will work for some of the follow- up positions still, isn't so bad. Chest isn't a matter of hardware, more of time you invest in the setting, regards

[Hobacle]

Thank you for any help you can offer.

forum3/viewtopic.php?p=920369#p920369

You're welcome

Oh no... I pasted the link wrongly... Thanks for the right link...

Welcome again

And one more help:
Take the position next to the one you want the DTM to prove for, try to figure out the Chest- params best to solve this one, then chance the setting will work for some of the follow- up positions still, isn't so bad. Chest isn't a matter of hardware, more of time you invest in the setting, regards

Several months ago I used Chest to do a 100-hour calculation, then my cpu burnt. That calculation was on a position which is much easier.

[peter]

Several months ago I used Chest to do a 100-hour calculation, then my cpu burnt. That calculation was on a position which is much easier.

Hope, you don't mean difficulty of position is to be converted directly to CPU- heat

100 hours shoud be 100 hours as for that and single thread (which Chest is anyhow) isn't a burner on its own for modern hardware normally, I suspect your CPU to having had its last 100 hours anyhow, no matter on what you would have spent them with

Anyhow, 100 hours at one positions is useless, if the setting doesn't find mate within 1 hour, try another one setting or a nearer to mate position in line. Peer or Jesus will be of better help in such cases than I am, my patience normally isn't big enough for such fiddling and my experience in Chest- params isn't neither.

If you give the line you think to be the shortest possible correct one, I'll try to see what I can do backsolving it with Huntsman and or other programs.

[Hobacle]

Several months ago I used Chest to do a 100-hour calculation, then my cpu burnt. That calculation was on a position which is much easier.

I suspect your CPU to having had its last 100 hours anyhow, no matter on what you would have spent them with

Perhaps.

[peter]

Several months ago I used Chest to do a 100-hour calculation, then my cpu burnt. That calculation was on a position which is much easier.

I suspect your CPU to having had its last 100 hours anyhow, no matter on what you would have spent them with

Perhaps.

Sorry, but I don't come any further, than I was already here then

forum3/viewtopic.php?p=920375&sid=0b604 ... 65#p920375

[Spliffjiffer]

2b1qrk1/4p3/3pPp1p/1pnP2p1/2p1P3/2P4P/2P1Q1PK/1B2BR2

The full pgn file of the #226:
[pgn][Event ""]
[Site ""]
[Date "2022.02.06"]
[Round ""]
[White ""]
[Black ""]
[Result "1-0"]
[FEN "1N2Q3/p6n/p5n1/p1p2rpb/p4k1r/K1P4p/2PP4/6B1 w - - 0 1"]
[SetUp "1"]

1. Bh2+ Kf3 2. Qe3+ Kg2 3. Qg1+ Kf3 4. Qf1+ Kg4 5. Qe2+ Rf3 6. Qe6+ Rf5 7. Nd7
Kf3 8. Qe3+ Kg2 9. Qg1+ Kf3 10. Qf1+ Kg4 11. Qe2+ Rf3 12. Qe6+ Rf5 13. Kb2 Kf3
14. Qe3+ Kg2 15. Qg1+ Kf3 16. Qf1+ Kg4 17. Qe2+ Rf3 18. Qe6+ Rf5 19. Kc1 Kf3
20. Qe3+ Kg2 21. Qg1+ Kf3 22. Qf1+ Kg4 23. Qe2+ Rf3 24. Qe6+ Rf5 25. Kd1 a3 26.
Kc1 Kf3 27. Qe3+ Kg2 28. Qg1+ Kf3 29. Qf1+ Kg4 30. Qe2+ Rf3 31. Qe6+ Rf5 32.
Kb1 Kf3 33. Qe3+ Kg2 34. Qg1+ Kf3 35. Qf1+ Kg4 36. Qe2+ Rf3 37. Qe6+ Rf5 38.
Ka2 Kf3 39. Qe3+ Kg2 40. Qg1+ Kf3 41. Qf1+ Kg4 42. Qe2+ Rf3 43. Qe6+ Rf5 44.
Kxa3 Kf3 45. Qe3+ Kg2 46. Qg1+ Kf3 47. Qf1+ Kg4 48. Qe2+ Rf3 49. Qe6+ Rf5 50.
Kb2 Kf3 51. Qe3+ Kg2 52. Qg1+ Kf3 53. Qf1+ Kg4 54. Qe2+ Rf3 55. Qe6+ Rf5 56.
Kc1 Kf3 57. Qe3+ Kg2 58. Qg1+ Kf3 59. Qf1+ Kg4 60. Qe2+ Rf3 61. Qe6+ Rf5 62.
Kd1 a4 63. Kc1 Kf3 64. Qe3+ Kg2 65. Qg1+ Kf3 66. Qf1+ Kg4 67. Qe2+ Rf3 68. Qe6+
Rf5 69. Kd1 a5 70. Kc1 Kf3 71. Qe3+ Kg2 72. Qg1+ Kf3 73. Qf1+ Kg4 74. Qe2+ Rf3
75. Qe6+ Rf5 76. Kd1 a6 77. Kc1 Kf3 78. Qe3+ Kg2 79. Qg1+ Kf3 80. Qf1+ Kg4 81.
Qe2+ Rf3 82. Qe6+ Rf5 83. Kd1 a3 84. Kc1 Kf3 85. Qe3+ Kg2 86. Qg1+ Kf3 87. Qf1+
Kg4 88. Qe2+ Rf3 89. Qe6+ Rf5 90. Kb1 Kf3 91. Qe3+ Kg2 92. Qg1+ Kf3 93. Qf1+
Kg4 94. Qe2+ Rf3 95. Qe6+ Rf5 96. Ka2 Kf3 97. Qe3+ Kg2 98. Qg1+ Kf3 99. Qf1+
Kg4 100. Qe2+ Rf3 101. Qe6+ Rf5 102. Kxa3 Kf3 103. Qe3+ Kg2 104. Qg1+ Kf3 105.
Qf1+ Kg4 106. Qe2+ Rf3 107. Qe6+ Rf5 108. Kb2 Kf3 109. Qe3+ Kg2 110. Qg1+ Kf3
111. Qf1+ Kg4 112. Qe2+ Rf3 113. Qe6+ Rf5 114. Kc1 Kf3 115. Qe3+ Kg2 116. Qg1+
Kf3 117. Qf1+ Kg4 118. Qe2+ Rf3 119. Qe6+ Rf5 120. Kd1 a4 121. Kc1 Kf3 122.
Qe3+ Kg2 123. Qg1+ Kf3 124. Qf1+ Kg4 125. Qe2+ Rf3 126. Qe6+ Rf5 127. Kd1 a5
128. Kc1 Kf3 129. Qe3+ Kg4 130. Qg1+ Kf3 131. Qf1+ Kg4 132. Qe2+ Rf3 133. Qe6+
Rf5 134. Kd1 a3 135. Kc1 Kf3 136. Qe3+ Kg2 137. Qg1+ Kf3 138. Qf1+ Kg4 139.
Qe2+ Rf3 140. Qe6+ Rf5 141. Kb1 Kf3 142. Qe3+ Kg2 143. Qg1+ Kf3 144. Qf1+ Kg4
145. Qe2+ Rf3 146. Qe6+ Rf5 147. Ka2 Kf3 148. Qe3+ Kg2 149. Qg1+ Kf3 150. Qf1+
Kg4 151. Qe2+ Rf3 152. Qe6+ Rf5 153. Kxa3 Kf3 154. Qe3+ Kg2 155. Qg1+ Kf3 156.
Qf1+ Kg4 157. Qe2+ Rf3 158. Qe6+ Rf5 159. Kb2 Kf3 160. Qe3+ Kg2 161. Qg1+ Kf3
162. Qf1+ Kg4 163. Qe2+ Rf3 164. Qe6+ Rf5 165. Kc1 Kf3 166. Qe3+ Kg2 167. Qg1+
Kf3 168. Qf1+ Kg4 169. Qe2+ Rf3 170. Qe6+ Rf5 171. Kd1 a4 172. Kc1 Kf3 173.
Qe3+ Kg2 174. Qg1+ Kf3 175. Qf1+ Kg4 176. Qe2+ Rf3 177. Qe6+ Rf5 178. Kd1 c4
179. Kc1 Kf3 180. Qe3+ Kg2 181. Qg1+ Kf3 182. Qf1+ Kg4 183. Qe2+ Rf3 184. Qe6+
Rf5 185. Kd1 a3 186. Kc1 Kf3 187. Qe3+ Kg2 188. Qg1+ Kf3 189. Qf1+ Kg4 190.
Qe2+ Rf3 191. Qe6+ Rf5 192. Kb1 Kf3 193. Qe3+ Kg2 194. Qg1+ Kf3 195. Qf1+ Kg4
196. Qe2+ Rf3 197. Qe6+ Rf5 198. Ka2 Kf3 199. Qe3+ Kg2 200. Qg1+ Kf3 201. Qf1+
Kg4 202. Qe2+ Rf3 203. Qe6+ Rf5 204. Kxa3 Kf3 205. Qe3+ Kg2 206. Qg1+ Kf3 207.
Qf1+ Kg4 208. Qe2+ Rf3 209. Qe6+ Rf5 210. Kb2 Kf3 211. Qe3+ Kg2 212. Qg1+ Kf3
213. Qf1+ Ke4 214. Qxc4+ Kf3 215. Qf1+ Kg4 216. Qe2+ Rf3 217. Qe6+ Rf5 218. Kc1
Kf3 219. Qe3+ Kg2 220. Qg1+ Kf3 221. Qf1+ Kg4 222. Qe2+ Rf3 223. Qe6+ Rf5 224.
Kd1 Nhf8 225. Nf6+ Kf3 226. Qe2# 1-0
[/pgn]

To finally prove this famous mate-in-226 composition has a shorter solution, we must simplify the work.

But it's still too hard for my hardware. So I need aid.
Thank you for any help you can offer.

the position is VERY conplex and Chest is no help here!
id like to suggest 2 things (after what ive read)...

1st:
my solution... "which is none...but its a request for help":

I believe that this is optimal:

1. Bh2+ Kf3 2. Qe3+ Kg2 3. Qg1+ Kf3 4. Qf1+ Kg4 5. Qe2+ Rf3 6. Qe6+ Rf5 7.
Nd7 Kf3 8. Qe3+ Kg2 9. Qg1+ Kf3 10. Qf1+ Kg4 11. Qe2+ Rf3 12. Qe6+ Rf5 13.
Kb2 c4 !?

my "solution" is this:

[pgn]
[Event "Computer Schach Partie"]
[Site "DESKTOP-F6DA4QS"]
[Date "2022.09.30"]
[Round "?"]
[White "Spliff"]
[Black "Spliff"]
[Result "1-0"]
[BlackElo "2400"]
[Time "22:32:19"]
[WhiteElo "2400"]
[SetUp "1"]
[FEN "1N2Q3/p6n/p5n1/p1p2rpb/p4k1r/K1P4p/2PP4/6B1 w - - 0 1"]
[Termination "normal"]
[PlyCount "251"]
[WhiteType "human"]
[BlackType "human"]

1. Bh2+ Kf3 2. Qe3+ Kg2 3. Qg1+ Kf3 4. Qf1+ Kg4 5. Qe2+ Rf3 6. Qe6+ Rf5 7.
Nd7 Kf3 8. Qe3+ Kg2 9. Qg1+ Kf3 10. Qf1+ Kg4 11. Qe2+ Rf3 12. Qe6+ Rf5 13.
Kb2 c4 14. Ka3 Kf3 15. Qe3+ Kg2 16. Qg1+ Kf3 17. Qf1+ Kg4 18. Qe2+ Rf3 19.
Qe6+ Rf5 20. Kxa4 Kf3 21. Qe3+ Kg2 22. Qg1+ Kf3 23. Qf1+ Kg4 24. Qe2+ Rf3
25. Qe6+ Rf5 26. Ka3 Kf3 27. Qe3+ Kg2 28. Qg1+ Kf3 29. Qf1+ Kg4 30. Qe2+
Rf3 31. Qe6+ Rf5 32. Kb2 Kf3 33. Qe3+ Kg2 34. Qg1+ Kf3 35. Qf1+ Kg4 36.
Qe2+ Rf3 37. Qe6+ Rf5 38. Kc1 Kf3 39. Qe3+ Kg2 40. Qg1+ Kf3 41. Qf1+ Kg4
42. Qe2+ Rf3 43. Qe6+ Rf5 44. Kd1 a4 45. Kc1 Kf3 46. Qe3+ Kg2 47. Qg1+ Kf3
48. Qf1+ Kg4 49. Qe2+ Rf3 50. Qe6+ Rf5 51. Kb2 Kf3 52. Qe3+ Kg2 53. Qg1+
Kf3 54. Qf1+ Kg4 55. Qe2+ Rf3 56. Qe6+ Rf5 57. Ka3 Kf3 58. Qe3+ Kg2 59.
Qg1+ Kf3 60. Qf1+ Kg4 61. Qe2+ Rf3 62. Qe6+ Rf5 63. Kxa4 Kf3 64. Qe3+ Kg2
65. Qg1+ Kf3 66. Qf1+ Kg4 67. Qe2+ Rf3 68. Qe6+ Rf5 69. Ka3 Kf3 70. Qe3+
Kg2 71. Qg1+ Kf3 72. Qf1+ Kg4 73. Qe2+ Rf3 74. Qe6+ Rf5 75. Kb2 Kf3 76.
Qe3+ Kg2 77. Qg1+ Kf3 78. Qf1+ Kg4 79. Qe2+ Rf3 80. Qe6+ Rf5 81. Kc1 a5 82.
d3 cxd3 83. cxd3 Kf3 84. Qe1 Rb5 85. c4 Nf4 86. Qf1+ Kg4 87. cxb5 Kf5 88.
Qf2 Ke6 89. Qxa7 Nxd3+ 90. Kc2 Bg6 91. Qb6+ Kf7 92. Kc3 Bf5 93. Qa7 Nf4 94.
b6 Nd5+ 95. Kb2 Rb4+ 96. Ka3 Ne7 97. Ne5+ Kf8 98. b7 Nf6 99. b8=Q+ Rxb8
100. Qxb8+ Kg7 101. Qc7 Nd5 102. Qc1 Nf4 103. Nf3 Kg6 104. Qc7 Nfd5 105.
Qd6+ Kf7 106. Nxg5+ Kf8 107. Qe5 Ke8 108. Qb8+ Bc8 109. Ne4 Kd7 110. Qb5+
Ke6 111. Nd6 Nb4 112. Nxc8 Nxc8 113. Qe5+ Kd7 114. Qc7+ Ke6 115. Qxc8+ Kf6
116. Ka4 Kg5 117. Kxa5 Na2 118. Qg8+ Kf5 119. Qxa2 Kf6 120. Qf2+ Kg6 121.
Qf1 Kg5 122. Qf7 Kg4 123. Qd5 Kh4 124. Qg8 Kh5 125. Bf4 h2 126. Qg5# 1-0

[/pgn]

im definately not sure about the correctness and its always difficult when things walk astray...
this cooked study gets weired for a headache at some points imo...
anyway: this is my proposal

2nd:
my doubghts:

44.d3!?! is a serious alternative in my eyes and i only noticed it but didnt check (any help here would be pretty much appreciated)


beyoned from that:
the pattern is amazing and i would like to mate in 225 moves (not 226!) [its about 13...c4 instead of 13...Kf3]

[Hobacle]

the position is VERY conplex and Chest is no help here!
id like to suggest 2 things (after what ive read)...

1st:
my solution... "which is none...but its a request for help":

I believe that this is optimal:

1. Bh2+ Kf3 2. Qe3+ Kg2 3. Qg1+ Kf3 4. Qf1+ Kg4 5. Qe2+ Rf3 6. Qe6+ Rf5 7.
Nd7 Kf3 8. Qe3+ Kg2 9. Qg1+ Kf3 10. Qf1+ Kg4 11. Qe2+ Rf3 12. Qe6+ Rf5 13.
Kb2 c4 !?

Well, I should say I believed the following was the solution after 13...c4:
[pgn][Event "?"]
[Site "?"]
[Date "2022.07.17"]
[Round "?"]
[White ""]
[Black ""]
[Result "1-0"]
[FEN "1N2Q3/p6n/p5n1/p1p2rpb/p4k1r/K1P4p/2PP4/6B1 w - - 0 1"]
[SetUp "1"]

1. Bh2+ Kf3 2. Qe3+ Kg2 3. Qg1+ Kf3 4. Qf1+ Kg4 5. Qe2+ Rf3 6. Qe6+ Rf5 7. Nd7
Kf3 8. Qe3+ Kg2 9. Qg1+ Kf3 10. Qf1+ Kg4 11. Qe2+ Rf3 12. Qe6+ Rf5 13. Kb2 c4
14. Ka3 Kf3 15. Qe3+ Kg2 16. Qg1+ Kf3 17. Qf1+ Kg4 18. Qe2+ Rf3 19. Qe6+ Rf5
20. Kxa4 Kf3 21. Qe3+ Kg2 22. Qg1+ Kf3 23. Qf1+ Kg4 (23... Ke4 {a}) 24. Qe2+
Rf3 25. Qe6+ Rf5 26. Ka3 Kf3 27. Qe3+ Kg2 28. Qg1+ Kf3 29. Qf1+ Kg4 30. Qe2+
Rf3 31. Qe6+ Rf5 32. Kb2 Kf3 33. Qe3+ Kg2 34. Qg1+ Kf3 35. Qf1+ Kg4 36. Qe2+
Rf3 37. Qe6+ Rf5 38. Kc1 Kf3 39. Qe3+ Kg2 40. Qg1+ Kf3 41. Qf1+ Kg4 42. Qe2+
Rf3 43. Qe6+ Rf5 44. Kd1 a4 45. Kc1 Kf3 46. Qe3+ Kg2 47. Qg1+ Kf3 48. Qf1+ Kg4
49. Qe2+ Rf3 50. Qe6+ Rf5 51. Kb2 Kf3 (51... a5 52. Ka3 Kf3 (52... a6 53. Kxa4
Kf3 54. Qe3+ Kg2 55. Qg1+ Kf3 56. Qf1+ Ke4 {b}) 53. Qe3+ Kg2 54. Qg1+ Kf3 55.
Qf1+ Kg4 56. Qe2+ Rf3 57. Qe6+ Rf5 58. Kxa4 Kf3 59. Qe3+ Kg2 60. Qg1+ Kf3 61.
Qf1+ Ke4 {c}) 52. Qe3+ Kg2 53. Qg1+ Kf3 54. Qf1+ Kg4 55. Qe2+ Rf3 56. Qe6+ Rf5
57. Ka3 Kf3 58. Qe3+ Kg2 59. Qg1+ Kf3 60. Qf1+ Kg4 61. Qe2+ Rf3 62. Qe6+ Rf5
63. Kxa4 Kf3 64. Qe3+ Kg2 65. Qg1+ Kf3 66. Qf1+ Kg4 (66... Ke4 {d}) 67. Qe2+
Rf3 68. Qe6+ Rf5 69. Ka3 Kf3 70. Qe3+ Kg2 71. Qg1+ Kf3 72. Qf1+ Kg4 73. Qe2+
Rf3 74. Qe6+ Rf5 75. Kb2 Kf3 76. Qe3+ Kg2 77. Qg1+ Kf3 78. Qf1+ Kg4 79. Qe2+
Rf3 80. Qe6+ Rf5 81. Kc1 a5 82. Kd1 a4 83. Kc1 Kf3 (83... a6 84. Kb2 Kf3 (84...
a5 85. Ka3 Kf3 86. Qe3+ Kg2 87. Qg1+ Kf3 88. Qf1+ Kg4 89. Qe2+ Rf3 90. Qe6+ Rf5
91. Kxa4 Kf3 92. Qe3+ Kg2 93. Qg1+ Kf3 94. Qf1+ Ke4 {e}) 85. Qe3+ Kg2 86. Qg1+
Kf3 87. Qf1+ Kg4 88. Qe2+ Rf3 89. Qe6+ Rf5 90. Ka3 Kf3 91. Qe3+ Kg2 92. Qg1+
Kf3 93. Qf1+ Kg4 94. Qe2+ Rf3 95. Qe6+ Rf5 96. Kxa4 Kf3 97. Qe3+ Kg2 98. Qg1+
Kf3 99. Qf1+ Ke4 {f}) 84. Qe3+ Kg2 85. Qg1+ Kf3 86. Qf1+ Kg4 87. Qe2+ Rf3 88.
Qe6+ Rf5 89. Kb2 Kf3 90. Qe3+ Kg2 91. Qg1+ Kf3 92. Qf1+ Kg4 93. Qe2+ Rf3 94.
Qe6+ Rf5 95. Ka3 Kf3 96. Qe3+ Kg2 97. Qg1+ Kf3 98. Qf1+ Kg4 99. Qe2+ Rf3 100.
Qe6+ Rf5 101. Kxa4 Kf3 102. Qe3+ Kg2 103. Qg1+ Kf3 104. Qf1+ Kg4 (104... Ke4
{g}) 105. Qe2+ Rf3 106. Qe6+ Rf5 107. Ka3 Kf3 108. Qe3+ Kg2 109. Qg1+ Kf3 110.
Qf1+ Kg4 111. Qe2+ Rf3 112. Qe6+ Rf5 113. Kb2 Kf3 114. Qe3+ Kg2 115. Qg1+ Kf3
116. Qf1+ Kg4 117. Qe2+ Rf3 118. Qe6+ Rf5 119. Kc1 a5 120. Kd1 a4 121. Kc1 Kf3
122. Qe3+ Kg2 123. Qg1+ Kf3 124. Qf1+ Kg4 125. Qe2+ Rf3 126. Qe6+ Rf5 127. Kd1
a3 128. Kc1 Kf3 129. Qe3+ Kg2 130. Qg1+ Kf3 131. Qf1+ Kg4 132. Qe2+ Rf3 133.
Qe6+ Rf5 134. Kb1 Kf3 135. Qe3+ Kg2 136. Qg1+ Kf3 137. Qf1+ Kg4 138. Qe2+ Rf3
139. Qe6+ Rf5 140. Ka2 Kf3 141. Qe3+ Kg2 142. Qg1+ Kf3 143. Qf1+ Kg4 144. Qe2+
Rf3 145. Qe6+ Rf5 146. Kxa3 Kf3 147. Qe3+ Kg2 148. Qg1+ Kf3 149. Qf1+ Kg4 150.
Qe2+ Rf3 151. Qe6+ Rf5 152. Kb2 Kf3 153. Qe3+ Kg2 154. Qg1+ Kf3 155. Qf1+ Ke4
156. Qxc4+ Kf3 157. Qf1+ Kg4 158. Qe2+ Rf3 159. Qe6+ Rf5 160. Kc1 Kf3 161. Qe3+
Kg2 162. Qg1+ Kf3 163. Qf1+ Kg4 164. Qe2+ Rf3 165. Qe6+ Rf5 166. Kd1 Nf6 167.
Nxf6+ Kf3 168. Qe2# 1-0

[/pgn]

And there were still 7 questionable lines as you can see.

But you find d3! , then the solution may be shortened even more. But this thing is less important now because we can (and only can) claim the cook after we find the correct shorter solution after 13...Kf3. I've simplified the 13...Kf3 line to the 17 positions above.