What is the most complex chess problem?

Question

There are many chess problems and studies that are very nuanced and can take ages to properly figure out.

What is the chess puzzle/problem with the longest (proven) solution?

Answer 1

If you're looking for the puzzle with the longest forced sequence, it would be this position ,which contains a win for white in 549 moves.

[FEN "1n1k4/6Q1/5KP1/8/7b/1r6/8/8 w - - 0 1"]

It was found by computers from the generation of 7-man endgame tablebases, and there are several similar positions with the same distance to mate.

If that seems a little extreme, then the longest mate puzzle made by a human was Otto Blathy's 'monster', which is a mate in 292 moves but contains an illegal starting position (i.e. it could never occur in a real game).

If you won't accept that, then here are the current record-holders for the longest puzzles created by a person from legal positions - A mate in 271 with 'obtrusive units' (legal, but must have come about through piece promotion, such as having two dark-squared bishops) and a mate in 267 without those. And, surprisingly, both of those were created by the same person.

As for the "most variations that don't work" as you stated, it's probably also the mate in 549 listed above, with the number of moves that would let the other player slip out or otherwise prolong the sequence even more.

Answer 2

Most complex problem I know of:

rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1

White to move.

Answer 3

The above problem is computer generated. The most complex man made chess puzzle is by David Zimbeck at www.zimbeckchess.com the main lines are always at least 30 or so moves with endings that take another 50 or so(so about 80-100 moves in total). Its starts with almost a full set of pieces and finishes with 3 knights and a pawn vs a queen and reduces to 3 knights vs a king.

I should add the link with the "longest" man made puzzles are not necessarily the most complex. The 271 length record by Petrovic is not actually complex because the moves repeat. Similar puzzles of length can be found in "Jeremy Morse Tasks and Records". The Zimbeck study has its complexity because there is many complicated sidelines.

If it doesnt have to be purely man made then yes, as the op said the 549 move tablebase currently is obviously the most complex.

http://www.zimbeckchess.com/1.htm

Answer 4

For the purpose of this answer, I'll guess that JMcPherson is asking for that chess problem that stipulates "White to play and mate in n" for the greatest possible n. Direct-mate in n, in other words.

There are chess problems with stipulations other than "White to play and mate in n", but let's stick to direct-mates for this answer.

For the problem to be sound, there must be a unique key (first move for White), and, after that, Black must be able to play in such a way that White is forced to go the whole n moves and never has a choice of move at any turn. Such a choice for White is known as a dual. We thus need the problem to be dual-free.

The tablebase mate in 549 cited by DTR is not a sound #549 problem because White can play in such a way that, on some occasions in the long solution line, every Black response which is strong enough to force White to go the full 549. moves gives White a choice (either on White's very next move or later). The same goes for the mates in 271 and 267 DTR mentioned.

One problem which has been cited as the longest dual-free direct-mate is the following.

[Title "Walther Jørgensen, Thema Danicum 26, Apr 1982, no.1921"]
[fen "1N2Q3/p6n/p5n1/p1p2rpb/p4k1r/K1P4p/2PP4/6B1 w - - 0 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+ Kg2 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+ Ke4! 183. Qxc4+ Kf3 184. Qf1+ Kg4 185. Qe2+ Rf3 186. Qe6+ Rf5 187. Kd1 a3 188. Kc1 Kf3 189. Qe3+ Kg2 190. Qg1+ Kf3 191. Qf1+ Kg4 192. Qe2+ Rf3 193. Qe6+ Rf5 194. Kb1 Kf3 195. Qe3+ Kg2 196. Qg1+ Kf3 197. Qf1+ Kg4 198. Qe2+ Rf3 199. Qe6+ Rf5 200. Ka2 Kf3 201. Qe3+ Kg2 202. Qg1+ Kf3 203. Qf1+ Kg4 204. Qe2+ Rf3 205. Qe6+ Rf5 206. Kxa3 Kf3 207. Qe3+ Kg2 208. Qg1+ Kf3 209. Qf1+ Kg4 210. Qe2+ Rf3 211. Qe6+ Rf5 212. Kb2 Kf3 213. Qe3+ Kg2 214. Qg1+ 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 Nf8,Nf6 225. Nf6+ Kf3 226. Qe2#

This problem is at PDB, from where I copied the moves. Morse lists it as the longest dual-free direct-mate; it is no. 741 in [1] and no. 865 in [2].

This problem is a 26-move extension of an earlier #200 by Jørgensen: Special Prize, Die Schwalbe, 1976. That problem is also at PDB, and is no. 740 in [1].

Is the #226 the record-holder? This web page at chessbase.com claims that the record-holder is a #203, which is Jørgensen's earlier #200 with a more modest 3-move extension by André Chéron. Now that chessbase.com web page is dated 2015. Has it cited information which is out-of-date? Or has the #226 been cooked? I don't know.

DTR cited a #292 by Otto Bláthy and correctly stated that its starting position is illegal. So to assess the above #226's acceptability, it is worth looking at its diagram to see if it is legal. It is, just. Four black pawns have made 8 captures b7xa6, c7xb6xa5, d7xc6xb5xa4, e7xd6xc5. White has 7 units, so those captures were of all but 1 of White's 9 missing units.

All those 8 captures were on the queenside, but White is missing all 4 kingside pawns. Black has 13 units, so White has made 3 captures. One was b2xc3, leaving 2. White could have also captured exd, but no more than 1 of White's kingside pawns can have made it to the queenside to be captured by a black pawn; no more than 1 was captured by a piece, so at least 2 had to promote.

It is just possible that only 2 White pawns promoted: the fP and gP. A piece captured White's hP. White's eP captured a piece on the d-file, then was captured by Black's eP on d7. White's gP captured Black's fP on the f-file, and White's fP and gP promoted on f8.

However, even if a problem's diagram cannot be reached without pawns promoting earlier in the game, that fact is not generally held against the problem, so long as it can be reached. What are regarded as blemishes are obtrusive pieces. Jørgensen's #226's diagram does not contain any obtrusive piece.

[1] Morse, Sir Jeremy. Chess Problems: Tasks & Records. 1st ed. Pub Faber & Faber, 1995. ISBN 0-571-15363-1

[2] Morse, Sir Jeremy. Chess Problems: Tasks & Records. 3rd ed. Pub Faber & Faber, 2016. ISBN 9781785891434

Answer 5

I know of a very complex selfmate with just 8 pieces on the board! I wouldn’t blame you if you couldn’t solve it yourself!

[Title "William Shinkman, 1907, Selfmate In 259 Moves"]
[FEN "8/8/8/8/QK6/1n6/B6R/r3k3 w - - 0 1"]

This position was originally published as a 423-mover initially, but then it was quickly changed to a 418-mover. It was then republished later on as a 298-mover after it was cooked by Joesph Babson and F.H. Curtiss. Nearly 80 years later, a further cook was found by Yaakov Mintz, and the 259 move solution was published in The Problemist 05/1985, on page 36.

Here is that solution.

[Title "Yaakov Mintz. After William Shinkman, 1985, Selfmate In 259 Moves"]
[FEN "8/8/8/8/QK6/1n6/B6R/r3k3 w - - 0 1"]

1. Qe8+ Kf1 2. Rh1+ Kf2 3. Qf7+ Kg2 4. Qd5+ Kg3 5. Qg5+ Kf3 6. Rh3+ Ke2 7. Qg4+ Kd2 8. Rh2+ Kc1 9. Qc4+ Kd1 10. Qc2+ Ke1 11. Qe4+ Kf1 12. Qf3+ Kg1 13. Qg3+ Kf1 14. Rh1+ Ke2 15. Qg2+ Ke3 16. Rh3+ Kf4 17. Rf3+ Ke5 18. Qg5+ Ke4 19. Qf4+ Kd5 20. Rd3+ Ke6 21. Rd6+ Ke7 22. Qf6+ Ke8 23. Re6+ Kd7 24. Qe7+ Kc8 25. Qe8+ Kc7 26. Rc6+ Kb7 27. Qd7+ Ka8 28. Ra6+ Kb8 29. Rb6+ Ka8 30. Qa4+ Na5 31. Ra6+ Kb8 32. Qe8+ Kb7 33. Qb5+ Kc8 34. Ra8+ Kc7 35. Qb8+ Kd7 36. Qd8+ Kc6 37. Ra6+ Kb7 38. Qb6+ Kc8 39. Ra8+ Kd7 40. Rd8+ Ke7 41. Qc7+ Kf6 42. Rf8+ Kg6 43. Qf7+ Kg5 44. Qf4+ Kg6 45. Rg8+ Kh5 46. Rh8+ Kg6 47. Qf7+ Kg5 48. Rh5+ Kg4 49. Qf5+ Kg3 50. Rh3+ Kg2 51. Bd5+ Kg1 52. Rg3+ Kh2 53. Rg2+ Kh1 54. Rg4+ Kh2 55. Qf4+ Kh3 56. Rg3+ Kh2 57. Re3+ Kg1 58. Qg3+ Kf1 59. Bg2+ Kg1 60. Bc6+ Kf1 61. Rf3+ Ke2 62. Qg2+ Ke1 63. Qg1+ Ke2 64. Rf2+ Ke3 65. Qg3+ Kd4 66. Qf4+ Kd3 67. Bb5+ Nc4 68. Qd2+ Ke4 69. Bc6+ Ke5 70. Qf4+ Ke6 71. Qf7+ Kd6 72. Qd7+ Ke5 73. Qg7+ Ke6 74. Rf6+ Ke5 75. Rf3+ Ke6 76. Qd7+ Ke5 77. Qe7+ Kd4 78. Qf6+ Ne5 79. Qh4+ Ng4 80. Qd8+ Ke5 81. Qg5+ Kd4 82. Qd2+ Ke5 83. Qf4+ Ke6 84. Qf5+ Kd6 85. Qc5+ Ke6 86. Bd5+ Ke5 87. Ba8+ Ke6 88. Qd5+ Ke7 89. Rf7+ Ke8 90. Qe6+ Kd8 91. Rd7+ Kc8 92. Bb7+ Kb8 93. Qe8+ Ka7 94. Be4+ Kb6 95. Rd6+ Kc7 96. Qc6+ Kb8 97. Qb6+ Kc8 98. Rc6+ Kd7 99. Bf5+ Ke8 100. Re6+ Kd7 101. Rf6+ Ke8 102. Qc6+ Ke7 103. Qd6+ Ke8 104. Re6+ Kf7 105. Qe7+ Kg8 106. Rg6+ Kh8 107. Qh4+ Nh6 108. Qd4+ Kh7 109. Rg7+ Kh8 110. Rb7+ Kg8 111. Bh7+ Kf8 112. Qh8+ Ng8 113. Qg7+ Ke8 114. Qg6+ Kd8 115. Qd6+ Kc8 116. Qc6+ Kd8 117. Rb8+ Ke7 118. Qc7+ Kf6 119. Rb6+ Kg5 120. Qg3+ Kh5 121. Qh3+ Kg5 122. Rg6+ Kf4 123. Qg3+ Kf5 124. Qg5+ Ke4 125. Rf6+ Kd4 126. Rf4+ Ke3 127. Qg3+ Kd2 128. Qc3+ Kd1 129. Qc2+ Ke1 130. Qf2+ Kd1 131. Qf1+ Kd2 132. Rf2+ Ke3 133. Re2+ Kd4 134. Re4+ Kd5 135. Qf7+ Kd6 136. Re6+ Kd5 137. Rb6+ Ke5 138. Qf5+ Kd4 139. Qf4+ Kd5 140. Be4+ Kd4 141. Bf3+ Kd3 142. Qe4+ Kd2 143. Qe2+ Kc1 144. Qe1+ Kb2 145. Qc3+ Ka2 146. Qa3+ Kb1 147. Kc5+ Kc2 148. Qb2+ Kd3 149. Qd4+ Kc2 150. Be4+ Kc1 151. Qg1+ Kd2 152. Rb2+ Kc3 153. Rc2+ Kb3 154. Qg3+ Ka4 155. Bc6+ Ka5 156. Qc7+ Ka6 157. Bb7+ Ka7 158. Qb6+ Kb8 159. Be4+ Kc8 160. Kd5+ Kd7 161. Qd6+ Ke8 162. Rc8+ Kf7 163. Qg6+ Ke7 164. Re8+ Kd7 165. Qe6+ Kc7 166. Qd6+ Kb7 167. Ke6+ Ka7 168. Qc5+ Ka6 169. Qc4+ Ka5 170. Ra8+ Kb6 171. Rb8+ Ka5 172. Rb5+ Ka6 173. Qc6+ Ka7 174. Rb7+ Ka8 175. Rh7+ Kb8 176. Qb6+ Kc8 177. Qb7+ Kd8 178. Qc7+ Ke8 179. Bc6+ Kf8 180. Qd6+ Ne7 181. Qb8+ Nc8 182. Rh8+ Kg7 183. Qb2+ Kg6 184. Be4+ Kg5 185. Qf6+ Kg4 186. Qf3+ Kg5 187. Qe3+ Kg4 188. Bf3+ Kg3 189. Bd5+ Kg4 190. Qf3+ Kg5 191. Rh5+ Kg6 192. Qf5+ Kg7 193. Qf6+ Kg8 194. Rg5+ Kh7 195. Rg7+ Kh8 196. Re7+ Kg8 197. Qf7+ Kh8 198. Qh5+ Kg8 199. Kd7+ Kf8 200. Rf7+ Kg8 201. Qg5+ Kh8 202. Rf8+ Kh7 203. Bg8+ Kh8 204. Bf7+ Kh7 205. Bg6+ Kg7 206. Qf6+ Kh6 207. Be8+ Kh7 208. Rf7+ Kg8 209. Qg5+ Kh8 210. Rf8+ Kh7 211. Qg8+ Kh6 212. Qh8+ Kg5 213. Qf6+ Kg4 214. Qf3+ Kh4 215. Qf2+ Kg5 216. Qe3+ Kh4 217. Rf4+ Kg5 218. Rc4+ Kf6 219. Qf3+ Ke5 220. Qe4+ Kf6 221. Qg6+ Ke5 222. Re4+ Kd5 223. Qe6+ Kc5 224. Rc4+ Kb5 225. Kd8+ Ka5 226. Rc5+ Kb4 227. Qc4+ Ka3 228. Ra5+ Kb2 229. Qb4+ Kc2 230. Rc5+ Kd3 231. Bb5+ Ke3232. Rc3+ Kd2 233. Qd4+ Ke1 234. Re3+ Kf2 235. Qd2+ Kg1 236. Rg3+ Kh1 237. Rh3+ Kg1 238. Qe3+ Kg2 239. Bc6+ Kf1 240. Rf3+ Kg2 241. Qd2+ Kh1 242. Rh3+ Kg1 243. Rg3+ Kf1 244. Bg2+ Kg1 245. Ba8+ Kf1 246. Rf3+ Kg1 247. Qf2+ Kh1 248. Rg3+ Rxa8 249. Qf1+ Kh2 250. Rg2+ Kh3 251. Qf3+ Kh4 252. Rh2+ Kg5 253. Rh5+ Kg6 254. Qg4+ Kf7 255. Rf5+ Ke6 256. Qe4+ Kd6 257. Qe5+ Kc6 258. Qb5+ Kd6 259. Qb6+ Nxb6#

Here is a Google Books link to my chosen source of an original publication (although it was also sent elsewhere by Shinkman), The British Chess Magazine Volume 27, See page 92, along with a Chess Problem Databse link.

In the 28th Volume, the 298-move cook was published on page 281.

The mentioned later republication of the problem but with the 298-move stipulation can be seen here, also on the Chess Problem Database. This is also where the 259-move solution, but with some changes in moves 5 to 10, in accordance to a comment left by Olaf Jenkner there.

Shinkman published a small bookelt in 1907 that explains the logic behind his selfmate, a PDF of which can be found here.

What a long problem for a position with just 8 pieces on the board!

Elsehwere

Answer 6

A certain similarity to @DTR's answer above which is mate in 1097 ply. This is mate in 1098 ply.

[Event "Black to play, mate in 1098 ply"]
[Site "?"]
[Date "2021.11.04"]
[Round "?"]
[White "martin"]
[Black "martin"]
[Result "*"]
[ECO "A00"]
[FEN "1n1k4/6Q1/5KP1/8/7Q/1r4b1/8/8 b - - 0 1"]
[startflipped ""]

1... Bxh4+{and_White_mates_in_549} (1... Rb6+ 2. Kf7+ Bxh4 (2...Kc8{c7} 3. Qxg3) 3. Qd4+ Kc7 4. g7 ) 
(1... Rf3+ 2. Ke6+ Bxh4 3. Qd4+ Ke8 4. g7 Rg3 (4... Rf6+ 5. Qxf6 Bxf6
6. g8=Q#)  (4... Nc6 5. Qd7#) 5. Qxh4 Rxg7 6. Qh8+ )  (1... Nd7+ 2.
Ke6+ Kc7 3. Qc4+ )

(In view of the threat 2.Qhh8# only the moves shown need be considered.)