6

What is the longest sequence of moves (by both White and Black) wherein White attempts to move one of their pieces from one square to another? Assume Black makes every move optimal towards the purpose of keeping White’s piece from reaching its intended square, but that it is nevertheless possible, in a finite number of moves, for White to achieve their purpose. If a complete response is impossible or impractical, partial/shorter responses are welcome.

For example, say that White’s goal is to get their King from e1 to g1 and can only achieve this through castling due to an unimpeded Black Rook on the second rank, but Black has an unimpeded Bishop on a6 controlling f1. White must remove the Bishop or the Rook from the diagonal in order to castle, which may take many moves.

Sorry if my question is vaguely worded or unclear in any way- I’ve never before written a chess-related problem. Also, feel free to edit the question or tags- all constructive criticism is welcomed.

  • Is my answer inline with your question? I just want to double check. – Rewan Demontay Dec 30 '19 at 0:50
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    All of the normal rules apply. As for both sides needing a king, I thought about it for a while, but I’ll say yes, both sides need a king. – Lieutenant Zipp Dec 30 '19 at 1:08
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    Yes. Pawns on their first rank may double-step. – Lieutenant Zipp Dec 30 '19 at 1:26
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    As I posted in a deleted answer, it is impossible to answer. Of the thousands of possible sequences of thousands of moves, we cannot verify there isn't one longer than whatever one we might come up with. Seems to me that when a question CANNOT be answered, saying so is the closest one can come to an answer. – WGroleau Dec 31 '19 at 5:28
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    @WGroleau Either that, or making as long of a sequence as you can think of, as I did. – Rewan Demontay Jan 1 at 16:03
11

Thanks for the fun question, and welcome to CSE!

For starters, the king is obviously the piece to choose. I will answer this question assuming that the normal rules of chess are used and no special conditions are used other than what the question has.

The OP has clarified that both sides need a king and first/last rank pawns can do a double step.

Assuming that you don’t mind illegal positons, here is my offering of 458 moves. White wants to move their king to the square a6, but it will take a long time.

I used a bit of a cheat, given how the replayer works, to show the double step for White’s a1 pawn.

Many thanks goes to @DM for their help calculating Black’s best defense during the last several moves of the game.

 [FEN "1P2pppp/Bk2pppp/1Pp1pppp/P1p1pppp/P1p5/P1p5/P1P5/PKP1pppp w - - 0 1"]

1. a6+ Kxa6 2. a5 Kb7 3. a6+ Kxa6 4. a4 Kb7 5. a5 Ka6 6. a4 Kb7 7. a6+ Kxa6 8. a5 Kb7 9. a6+ Kxa6 10. a2 Kb7 11. a4 Ka6 12. a5 Kb7 13. a6+ Kxa6 14. Ka2 Kb7 15. Ka3 Ka6 16. Ka4 Kb7 17. Ka5 f4 18. Ka4 Ka6 19. Ka3 Kb7 20. Ka2 Ka6 21. Ka1 Kb7 22. Kb1 Ka6 23. Ka2 Kb7 24. Ka3 Ka6 25. Ka4 Kb7 26. Ka5 f3 27. Ka4 Ka6 28. Ka3 Kb7 29. Ka2 Ka6 30. Ka1 Kb7 31. Kb1 Ka6 32. Ka2 Kb7 33. Ka3 Ka6 34. Ka4 Kb7 35. Ka5 f2 36. Ka4 Ka6 37. Ka3 Kb7 38. Ka2 Ka6 39. Ka1 Kb7 40. Kb1 Ka6 41. Ka2 Kb7 42. Ka3 Ka6 43. Ka4 Kb7 44. Ka5 f5 45. Ka4 Ka6 46. Ka3 Kb7 47. Ka2 Ka6 48. Ka1 Kb7 49. Kb1 Ka6 50. Ka2 Kb7 51. Ka3 Ka6 52. Ka4 Kb7 53. Ka5 f4 54. Ka4 Ka6 55. Ka3 Kb7 56. Ka2 Ka6 57. Ka1 Kb7 58. Kb1 Ka6 59. Ka2 Kb7 60. Ka3 Ka6 61. Ka4 Kb7 62. Ka5 f3 63. Ka4 Ka6 64. Ka3 Kb7 65. Ka2 Ka6 66. Ka1 Kb7 67. Kb1 Ka6 68. Ka2 Kb7 69. Ka3 Ka6 70. Ka4 Kb7 71. Ka5 f6 72. Ka4 Ka6 73. Ka3 Kb7 74. Ka2 Ka6 75. Ka1 Kb7 76. Kb1 Ka6 77. Ka2 Kb7 78. Ka3 Ka6 79. Ka4 Kb7 80. Ka5 f5 81. Ka4 Ka6 82. Ka3 Kb7 83. Ka2 Ka6 84. Ka1 Kb7 85. Kb1 Ka6 86. Ka2 Kb7 87. Ka3 Ka6 88. Ka4 Kb7 89. Ka5 f4 90. Ka4 Ka6 91. Ka3 Kb7 92. Ka2 Ka6 93. Ka1 Kb7 94. Kb1 Ka6 95. Ka2 Kb7 96. Ka3 Ka6 97. Ka4 Kb7 98. Ka5 f7 99. Ka4 Ka6 100. Ka3 Kb7 101. Ka2 Ka6 102. Ka1 Kb7 103. Kb1 Ka6 104. Ka2 Kb7 105. Ka3 Ka6 106. Ka4 Kb7 107. Ka5 f6 108. Ka4 Ka6 109. Ka3 Kb7 110. Ka2 Ka6 111. Ka1 Kb7 112. Kb1 Ka6 113. Ka2 Kb7 114. Ka3 Ka6 115. Ka4 Kb7 116. Ka5 f5 117. Ka4 Ka6 118. Ka3 Kb7 119. Ka2 Ka6 120. Ka1 Kb7 121. Kb1 Ka6 122. Ka2 Kb7 123. Ka3 Ka6 124. Ka4 Kb7 125. Ka5 h4 126. Ka4 Ka6 127. Ka3 Kb7 128. Ka2 Ka6 129. Ka1 Kb7 130. Kb1 Ka6 131. Ka2 Kb7 132. Ka3 Ka6 133. Ka4 Kb7 134. Ka5 h3 135. Ka4 Ka6 136. Ka3 Kb7 137. Ka2 Ka6 138. Ka1 Kb7 139. Kb1 Ka6 140. Ka2 Kb7 141. Ka3 Ka6 142. Ka4 Kb7 143. Ka5 h2 144. Ka4 Ka6 145. Ka3 Kb7 146. Ka2 Ka6 147. Ka1 Kb7 148. Kb1 Ka6 149. Ka2 Kb7 150. Ka3 Ka6 151. Ka4 Kb7 152. Ka5 h5 153. Ka4 Ka6 154. Ka3 Kb7 155. Ka2 Ka6 156. Ka1 Kb7 157. Kb1 Ka6 158. Ka2 Kb7 159. Ka3 Ka6 160. Ka4 Kb7 161. Ka5 h4  162. Ka4 Ka6 163. Ka3 Kb7 164. Ka2 Ka6 165. Ka1 Kb7 166. Kb1 Ka6 167. Ka2 Kb7 168. Ka3 Ka6 169. Ka4 Kb7 170. Ka5 h3 171. Ka4 Ka6 172. Ka3 Kb7 173. Ka2 Ka6  174. Ka1 Kb7 175. Kb1 Ka6 176. Ka2 Kb7 177. Ka3 Ka6 178. Ka4 Kb7 179. Ka5 h6 180. Ka4 Ka6 181. Ka3 Kb7 182. Ka2 Ka6 183. Ka1 Kb7 184. Kb1 Ka6 185. Ka2 Kb7 186. Ka3 Ka6 187. Ka4 Kb7 188. Ka5 h5 189. Ka4 Ka6 190. Ka3 Kb7 191. Ka2 Ka6 192. Ka1 Kb7 193. Kb1 Ka6 194. Ka2 Kb7 195. Ka3 Ka6 196. Ka4 Kb7 197. Ka5 h4 198. Ka4 Ka6 199. Ka3 Kb7 200. Ka2 Ka6 201. Ka1 Kb7 202. Kb1 Ka6 203. Ka2 Kb7 204. Ka3 Ka6 205. Ka4 Kb7 206. Ka5 h7 207. Ka4 Ka6 208. Ka3 Kb7 209. Ka2 Ka6 210. Ka1 Kb7 211. Kb1 Ka6 212. Ka2 Kb7 213. Ka3 Ka6 214. Ka4 Kb7 215. Ka5 h6 216. Ka4 Ka6 217. Ka3 Kb7 218. Ka2 Ka6 219. Ka1 Kb7 220. Kb1 Ka6 221. Ka2 Kb7 222. Ka3 Ka6 223. Ka4 Kb7 224. Ka5 h5 225. Ka4 Ka6 226. Ka3 Kb7 227. Ka2 Ka6 228. Ka1 Kb7 229. Kb1 Ka6 230. Ka2 Kb7 231. Ka3 Ka6 232. Ka4 Kb7 233. Ka5 g4 234. Ka4 Ka6 235. Ka3 Kb7 236. Ka2 Ka6 237. Ka1 Kb7 238. Kb1 Ka6 239. Ka2 Kb7 240. Ka3 Ka6 241. Ka4 Kb7 242. Ka5 g3 243. Ka4 Ka6 244. Ka3 Kb7 245. Ka2 Ka6 246. Ka1 Kb7 247. Kb1 Ka6 248. Ka2 Kb7 249. Ka3 Ka6 250. Ka4 Kb7 251. Ka5 g2 252. Ka4 Ka6 253. Ka3 Kb7 254. Ka2 Ka6 255. Ka1 Kb7 256. Kb1 Ka6 257. Ka2 Kb7 258. Ka3 Ka6 259. Ka4 Kb7 260. Ka5 g5 261. Ka4 Ka6 262. Ka3 Kb7 263. Ka2 Ka6 264. Ka1 Kb7 265. Kb1 Ka6 266. Ka2 Kb7 267. Ka3 Ka6 268. Ka4 Kb7 269. Ka5 g4 270. Ka4 Ka6 271. Ka3 Kb7 272. Ka2 Ka6 273. Ka1 Kb7 274. Kb1 Ka6 275. Ka2 Kb7 276. Ka3 Ka6 277. Ka4 Kb7 278. Ka5 g3 279. Ka4 Ka6 280. Ka3 Kb7 281. Ka2 Ka6 282. Ka1 Kb7 283. Kb1 Ka6 284. Ka2 Kb7 285. Ka3 Ka6 286. Ka4 Kb7 287. Ka5 g6 288. Ka4 Ka6 289. Ka3 Kb7 290. Ka2 Ka6 291. Ka1 Kb7 292. Kb1 Ka6 293. Ka2 Kb7 294. Ka3 Ka6 295. Ka4 Kb7 296. Ka5 g5 297. Ka4 Ka6 298. Ka3 Kb7 299. Ka2 Ka6 300. Ka1 Kb7 301. Kb1 Ka6 302. Ka2 Kb7 303. Ka3 Ka6 304. Ka4 Kb7 305. Ka5 g4 306. Ka4 Ka6 307. Ka3 Kb7 308. Ka2 Ka6 309. Ka1 Kb7 310. Kb1 Ka6 311. Ka2 Kb7 312. Ka3 Ka6 313. Ka4 Kb7 314. Ka5 g7 315. Ka4 Ka6 316. Ka3 Kb7 317. Ka2 Ka6 318. Ka1 Kb7 319. Kb1 Ka6 320. Ka2 Kb7 321. Ka3 Ka6 322. Ka4 Kb7 323. Ka5 g6 324. Ka4 Ka6 325. Ka3 Kb7 326. Ka2 Ka6 327. Ka1 Kb7 328. Kb1 Ka6 329. Ka2 Kb7 330. Ka3 Ka6 331. Ka4 Kb7 332. Ka5 g5 333. Ka4 Ka6 334. Ka3 Kb7 335. Ka2 Ka6 336. Ka1 Kb7 337. Kb1 Ka6 338. Ka2 Kb7 339. Ka3 Ka6 340. Ka4 Kb7 341. Ka5 e4 342. Ka4 Ka6 343. Ka3 Kb7 344. Ka2 Ka6 345. Ka1 Kb7 346. Kb1 Ka6 347. Ka2 Kb7 348. Ka3 Ka6 349. Ka4 Kb7 350. Ka5 e3 351. Ka4 Ka6 352. Ka3 Kb7 353. Ka2 Ka6 354. Ka1 Kb7 355. Kb1 Ka6 356. Ka2 Kb7 357. Ka3 Ka6 358. Ka4 Kb7 359. Ka5 e2 360. Ka4 Ka6 361. Ka3 Kb7 362. Ka2 Ka6 363. Ka1 Kb7 364. Kb1 Ka6 365. Ka2 Kb7 366. Ka3 Ka6 367. Ka4 Kb7 368. Ka5 e5 369. Ka4 Ka6 370. Ka3 Kb7 371. Ka2 Ka6 372. Ka1 Kb7 373. Kb1 Ka6 374. Ka2 Kb7 375. Ka3 Ka6 376. Ka4 Kb7 377. Ka5 e4 378. Ka4 Ka6 379. Ka3 Kb7 380. Ka2 Ka6 381. Ka1 Kb7 382. Kb1 Ka6 383. Ka2 Kb7 384. Ka3 Ka6 385. Ka4 Kb7 386. Ka5 e3 387. Ka4 Ka6 388. Ka3 Kb7 389. Ka2 Ka6 390. Ka1 Kb7 391. Kb1 Ka6 392. Ka2 Kb7 393. Ka3 Ka6 394. Ka4 Kb7 395. Ka5 e6 396. Ka4 Ka6 397. Ka3 Kb7 398. Ka2 Ka6 399. Ka1 Kb7 400. Kb1 Ka6 401. Ka2 Kb7 402. Ka3 Ka6 403. Ka4 Kb7 404. Ka5 e5 405. Ka4 Ka6 406. Ka3 Kb7 407. Ka2 Ka6 408. Ka1 Kb7 409. Kb1 Ka6 410. Ka2 Kb7 411. Ka3 Ka6 412. Ka4 Kb7 413. Ka5 e4 414. Ka4 Ka6 415. Ka3 Kb7 416. Ka2 Ka6 417. Ka1 Kb7 418. Kb1 Ka6 419. Ka2 Kb7 420. Ka3 Ka6 421. Ka4 Kb7 422. Ka5 e7 423. Ka4 Ka6 424. Ka3 Kb7 425. Ka2 Ka6 426. Ka1 Kb7 427. Kb1 Ka6 428. Ka2 Kb7 429. Ka3 Ka6 430. Ka4 Kb7 431. Ka5 e6 432. Ka4 Ka6 433. Ka3 Kb7 434. Ka2 Ka6 435. Ka1 Kb7 436. Kb1 Ka6 437. Ka2 Kb7 438. Ka3 Ka6 439. Ka4 Kb7 440. Ka5 e5 441. Ka4 Ka6 442. Ka3 Kb7 443. Ka2 Ka6 444. Ka1 Kb7 445. Kb1 Ka6 446. Ka2 Ka5 447. Ka3 Kb5 448. b7 Ka6 449. Bxc5 Kb5 450. Be7 Ka5 451. Bd8+ Kb5 452. Bc7 c5 453. Bd8 Ka6 454. Ka4 Kxb7 455. Kb5 Ka7 456. Bb6+ Kb7 457. Bxc5 Kc7 458. Ka6

As for a legal postion, 64 moves is the longest I have come up with so far. White wants to move their king to f2.

[FEN "5b1k/2p1pBp1/1pPpP1P1/1P1p4/8/7p/6pP/3n2K1 w - - 0 1"]

1. Be8 Kg8 2. Bd7 Kh8 3. Bc8 Kg8 4. Ba6 Kh8 5. Bb7 Kg8 6. Bc8 Kh8 7. Bd7 Kg8 8. Be8 Kh8 9. Bf7 d4 10. Be8 Kg8 11. Bd7 Kh8 12. Bc8 Kg8 13. Ba6 Kh8 14. Bb7 Kg8 15. Bc8 Kh8 16. Bd7 Kg8 17. Be8 Kh8 18. Bf7 d3 19. Be8 Kg8 20. Bd7 Kh8 21. Bc8 Kg8 22. Ba6 Kh8 23. Bb7 Kg8 24. Bc8 Kh8 25. Bd7 Kg8 26. Be8 Kh8 27. Bf7 d2 28. Be8 Kg8 29. Bd7 Kh8 30. Bc8 Kg8 31. Ba6 Kh8 32. Bb7 Kg8 33. Bc8 Kh8 34. Bd7 Kg8 35. Be8 Kh8 36. Bf7 d5 37. Be8 Kg8 38. Bd7 Kh8 39. Bc8 Kg8 40. Ba6 Kh8 41. Bb7 Kg8 42. Bc8 Kh8 43. Bd7 Kg8 44. Be8 Kh8 45. Bf7 d4 46. Be8 Kg8 47. Bd7 Kh8 48. Bc8 Kg8 49. Ba6 Kh8 50. Bb7 Kg8 51. Bc8 Kh8 52. Bd7 Kg8 53. Be8 Kh8 54. Bf7 d3 55. Be8 Kg8 56. Bd7 Kh8 57. Bc8 Kg8 58. Ba6 Kh8 59. Bb7 Kg8 60. Bc8 Kh8 61. Bd7 Kg8 62. Be8 Kh8 63. Bf7 Ne3 64. Kf2
  • 1
    Hmm... what if Black plays 231...Ka5? Sure, the pawn will promote quickly, but it keeps the White king out of a6 longer than the text, as far as I can tell. – D M Dec 30 '19 at 2:10
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    446, now. It's when all Black pawns are fixed and White has regained the opposition with his king. – D M Dec 30 '19 at 2:31
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    That underpromotion is nice, yes. I was looking at a queen promotion originally and that takes longer. As it is, I only managed to delay it a couple of moves :) – D M Dec 30 '19 at 2:44
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    @DM I might have a simple fix for that-just add a White pawn on b8. Now if Black King moves too far. the. Bishop will get out and the White king will make it to a6 in less than 453 moves. – Rewan Demontay Dec 30 '19 at 3:30
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    Nice. Don't forget to edit the ending, since the promotion is now invalid since a pawn is already there. I suggest 449.Bxc5. – D M Dec 30 '19 at 3:39
4

The best example I could find in PDB is this one:

[Title "Theodor Steudel: Problemkiste 66, Dec 1989, no. 2339. Za6 in 12"]
[StartFlipped "0"]
[fen "8/1p1p1p2/1P1P1P1P/8/p7/p1p1p1p1/2P1P1P1/k1K w K - 0 1"]

1.h7 a2 2.h8=N a3 3.Ng6 fxg6 4.f7 g5 5.f8=N g4 6.Ne6 dxe6
7.d7 e5 8.d8=N e4 9.Nc6 bxc6 10.b7 c5 11.b8=N c4 12.Na6

(Far greater lengths are possible in series-problems.)

  • How did you find this? – Rewan Demontay Dec 31 '19 at 20:29
  • By looking in PDB. PDB uses e.g. "Za6 in 12" to mean "Show how White can move a unit to a6 within 12 moves, against any defence from Black". Stipulations like this may be preceded by "s" for "self" or "h" for "help", and further preceded by "ser-" for "series". Problems whose stipulations have any of those prefixes must be ignored because the OP wasn't about them. – Rosie F Jan 1 at 7:21
3

It depends on the exact position.

If white only has the king left, and in your position black only their rook, bishop and king, then it would take forever. Or at least untill the 50 move rule kicks in. Give black more pawns and each one of their moves could add another 50 to the duration.

With more pieces and or pawns it might take more or less time.

For example, let’s say it’s White to move the queen’s rook pawn to a8 from the normal starting position.

There is no way black can keep it from getting captured. Thus the pawn never gets to a8. The number of moves is equivalent to infinity.

  • 1
    Well, to answer your first issue, I mentioned that it should be possible, in a FINITE number of moves, for White to achieve their goal. – Lieutenant Zipp Dec 30 '19 at 0:20
  • 1
    Of course the answer depends on the position and the maneuvering piece. Also, the 50-move rule guarantees that my query even HAS a finite solution. My question has whatever solution it has because of your objections, not in spite of them. – Lieutenant Zipp Dec 30 '19 at 1:03
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    I am saying there is no way to know the solution in our lifetime unless you specify a specific position. – yobamamama Dec 30 '19 at 1:06
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    @yobamamama That’s the point-to have fun trying to find the maximum. You are right that we will never truly know. It’s a challenging puzzle that’s fun to attempt to figure out. – Rewan Demontay Dec 30 '19 at 1:09
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    In that case, partial solutions in the vein of Rewan’s answer would suffice. – Lieutenant Zipp Dec 30 '19 at 1:10

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