Tower of Hanoi with 9 Disks
The shortest solution is 511 moves. Play them on the board, or read every one in the list under it.
Optimal solution
511moves2⁹ − 1
- First move
- Disk 1, A → C
- At one move a second
- 8 minutes
- Difficulty
- Expert
9 disks on tower A. 511 moves to go.Step 0 of 511
| Move | Disk | From | To |
|---|---|---|---|
| 1 | 1 | A | C |
| 2 | 2 | A | B |
| 3 | 1 | C | B |
| 4 | 3 | A | C |
| 5 | 1 | B | A |
| 6 | 2 | B | C |
| 7 | 1 | A | C |
| 8 | 4 | A | B |
| 9 | 1 | C | B |
| 10 | 2 | C | A |
| 11 | 1 | B | A |
| 12 | 3 | C | B |
| 13 | 1 | A | C |
| 14 | 2 | A | B |
| 15 | 1 | C | B |
| 16 | 5 | A | C |
| 17 | 1 | B | A |
| 18 | 2 | B | C |
| 19 | 1 | A | C |
| 20 | 3 | B | A |
| 21 | 1 | C | B |
| 22 | 2 | C | A |
| 23 | 1 | B | A |
| 24 | 4 | B | C |
| 25 | 1 | A | C |
| 26 | 2 | A | B |
| 27 | 1 | C | B |
| 28 | 3 | A | C |
| 29 | 1 | B | A |
| 30 | 2 | B | C |
| 31 | 1 | A | C |
| 32 | 6 | A | B |
| 33 | 1 | C | B |
| 34 | 2 | C | A |
| 35 | 1 | B | A |
| 36 | 3 | C | B |
| 37 | 1 | A | C |
| 38 | 2 | A | B |
| 39 | 1 | C | B |
| 40 | 4 | C | A |
| 41 | 1 | B | A |
| 42 | 2 | B | C |
| 43 | 1 | A | C |
| 44 | 3 | B | A |
| 45 | 1 | C | B |
| 46 | 2 | C | A |
| 47 | 1 | B | A |
| 48 | 5 | C | B |
| 49 | 1 | A | C |
| 50 | 2 | A | B |
| 51 | 1 | C | B |
| 52 | 3 | A | C |
| 53 | 1 | B | A |
| 54 | 2 | B | C |
| 55 | 1 | A | C |
| 56 | 4 | A | B |
| 57 | 1 | C | B |
| 58 | 2 | C | A |
| 59 | 1 | B | A |
| 60 | 3 | C | B |
| 61 | 1 | A | C |
| 62 | 2 | A | B |
| 63 | 1 | C | B |
| 64 | 7 | A | C |
| 65 | 1 | B | A |
| 66 | 2 | B | C |
| 67 | 1 | A | C |
| 68 | 3 | B | A |
| 69 | 1 | C | B |
| 70 | 2 | C | A |
| 71 | 1 | B | A |
| 72 | 4 | B | C |
| 73 | 1 | A | C |
| 74 | 2 | A | B |
| 75 | 1 | C | B |
| 76 | 3 | A | C |
| 77 | 1 | B | A |
| 78 | 2 | B | C |
| 79 | 1 | A | C |
| 80 | 5 | B | A |
| 81 | 1 | C | B |
| 82 | 2 | C | A |
| 83 | 1 | B | A |
| 84 | 3 | C | B |
| 85 | 1 | A | C |
| 86 | 2 | A | B |
| 87 | 1 | C | B |
| 88 | 4 | C | A |
| 89 | 1 | B | A |
| 90 | 2 | B | C |
| 91 | 1 | A | C |
| 92 | 3 | B | A |
| 93 | 1 | C | B |
| 94 | 2 | C | A |
| 95 | 1 | B | A |
| 96 | 6 | B | C |
| 97 | 1 | A | C |
| 98 | 2 | A | B |
| 99 | 1 | C | B |
| 100 | 3 | A | C |
| 101 | 1 | B | A |
| 102 | 2 | B | C |
| 103 | 1 | A | C |
| 104 | 4 | A | B |
| 105 | 1 | C | B |
| 106 | 2 | C | A |
| 107 | 1 | B | A |
| 108 | 3 | C | B |
| 109 | 1 | A | C |
| 110 | 2 | A | B |
| 111 | 1 | C | B |
| 112 | 5 | A | C |
| 113 | 1 | B | A |
| 114 | 2 | B | C |
| 115 | 1 | A | C |
| 116 | 3 | B | A |
| 117 | 1 | C | B |
| 118 | 2 | C | A |
| 119 | 1 | B | A |
| 120 | 4 | B | C |
| 121 | 1 | A | C |
| 122 | 2 | A | B |
| 123 | 1 | C | B |
| 124 | 3 | A | C |
| 125 | 1 | B | A |
| 126 | 2 | B | C |
| 127 | 1 | A | C |
| 128 | 8 | A | B |
| 129 | 1 | C | B |
| 130 | 2 | C | A |
| 131 | 1 | B | A |
| 132 | 3 | C | B |
| 133 | 1 | A | C |
| 134 | 2 | A | B |
| 135 | 1 | C | B |
| 136 | 4 | C | A |
| 137 | 1 | B | A |
| 138 | 2 | B | C |
| 139 | 1 | A | C |
| 140 | 3 | B | A |
| 141 | 1 | C | B |
| 142 | 2 | C | A |
| 143 | 1 | B | A |
| 144 | 5 | C | B |
| 145 | 1 | A | C |
| 146 | 2 | A | B |
| 147 | 1 | C | B |
| 148 | 3 | A | C |
| 149 | 1 | B | A |
| 150 | 2 | B | C |
| 151 | 1 | A | C |
| 152 | 4 | A | B |
| 153 | 1 | C | B |
| 154 | 2 | C | A |
| 155 | 1 | B | A |
| 156 | 3 | C | B |
| 157 | 1 | A | C |
| 158 | 2 | A | B |
| 159 | 1 | C | B |
| 160 | 6 | C | A |
| 161 | 1 | B | A |
| 162 | 2 | B | C |
| 163 | 1 | A | C |
| 164 | 3 | B | A |
| 165 | 1 | C | B |
| 166 | 2 | C | A |
| 167 | 1 | B | A |
| 168 | 4 | B | C |
| 169 | 1 | A | C |
| 170 | 2 | A | B |
| 171 | 1 | C | B |
| 172 | 3 | A | C |
| 173 | 1 | B | A |
| 174 | 2 | B | C |
| 175 | 1 | A | C |
| 176 | 5 | B | A |
| 177 | 1 | C | B |
| 178 | 2 | C | A |
| 179 | 1 | B | A |
| 180 | 3 | C | B |
| 181 | 1 | A | C |
| 182 | 2 | A | B |
| 183 | 1 | C | B |
| 184 | 4 | C | A |
| 185 | 1 | B | A |
| 186 | 2 | B | C |
| 187 | 1 | A | C |
| 188 | 3 | B | A |
| 189 | 1 | C | B |
| 190 | 2 | C | A |
| 191 | 1 | B | A |
| 192 | 7 | C | B |
| 193 | 1 | A | C |
| 194 | 2 | A | B |
| 195 | 1 | C | B |
| 196 | 3 | A | C |
| 197 | 1 | B | A |
| 198 | 2 | B | C |
| 199 | 1 | A | C |
| 200 | 4 | A | B |
| 201 | 1 | C | B |
| 202 | 2 | C | A |
| 203 | 1 | B | A |
| 204 | 3 | C | B |
| 205 | 1 | A | C |
| 206 | 2 | A | B |
| 207 | 1 | C | B |
| 208 | 5 | A | C |
| 209 | 1 | B | A |
| 210 | 2 | B | C |
| 211 | 1 | A | C |
| 212 | 3 | B | A |
| 213 | 1 | C | B |
| 214 | 2 | C | A |
| 215 | 1 | B | A |
| 216 | 4 | B | C |
| 217 | 1 | A | C |
| 218 | 2 | A | B |
| 219 | 1 | C | B |
| 220 | 3 | A | C |
| 221 | 1 | B | A |
| 222 | 2 | B | C |
| 223 | 1 | A | C |
| 224 | 6 | A | B |
| 225 | 1 | C | B |
| 226 | 2 | C | A |
| 227 | 1 | B | A |
| 228 | 3 | C | B |
| 229 | 1 | A | C |
| 230 | 2 | A | B |
| 231 | 1 | C | B |
| 232 | 4 | C | A |
| 233 | 1 | B | A |
| 234 | 2 | B | C |
| 235 | 1 | A | C |
| 236 | 3 | B | A |
| 237 | 1 | C | B |
| 238 | 2 | C | A |
| 239 | 1 | B | A |
| 240 | 5 | C | B |
| 241 | 1 | A | C |
| 242 | 2 | A | B |
| 243 | 1 | C | B |
| 244 | 3 | A | C |
| 245 | 1 | B | A |
| 246 | 2 | B | C |
| 247 | 1 | A | C |
| 248 | 4 | A | B |
| 249 | 1 | C | B |
| 250 | 2 | C | A |
| 251 | 1 | B | A |
| 252 | 3 | C | B |
| 253 | 1 | A | C |
| 254 | 2 | A | B |
| 255 | 1 | C | B |
| 256 | 9 | A | C |
| 257 | 1 | B | A |
| 258 | 2 | B | C |
| 259 | 1 | A | C |
| 260 | 3 | B | A |
| 261 | 1 | C | B |
| 262 | 2 | C | A |
| 263 | 1 | B | A |
| 264 | 4 | B | C |
| 265 | 1 | A | C |
| 266 | 2 | A | B |
| 267 | 1 | C | B |
| 268 | 3 | A | C |
| 269 | 1 | B | A |
| 270 | 2 | B | C |
| 271 | 1 | A | C |
| 272 | 5 | B | A |
| 273 | 1 | C | B |
| 274 | 2 | C | A |
| 275 | 1 | B | A |
| 276 | 3 | C | B |
| 277 | 1 | A | C |
| 278 | 2 | A | B |
| 279 | 1 | C | B |
| 280 | 4 | C | A |
| 281 | 1 | B | A |
| 282 | 2 | B | C |
| 283 | 1 | A | C |
| 284 | 3 | B | A |
| 285 | 1 | C | B |
| 286 | 2 | C | A |
| 287 | 1 | B | A |
| 288 | 6 | B | C |
| 289 | 1 | A | C |
| 290 | 2 | A | B |
| 291 | 1 | C | B |
| 292 | 3 | A | C |
| 293 | 1 | B | A |
| 294 | 2 | B | C |
| 295 | 1 | A | C |
| 296 | 4 | A | B |
| 297 | 1 | C | B |
| 298 | 2 | C | A |
| 299 | 1 | B | A |
| 300 | 3 | C | B |
| 301 | 1 | A | C |
| 302 | 2 | A | B |
| 303 | 1 | C | B |
| 304 | 5 | A | C |
| 305 | 1 | B | A |
| 306 | 2 | B | C |
| 307 | 1 | A | C |
| 308 | 3 | B | A |
| 309 | 1 | C | B |
| 310 | 2 | C | A |
| 311 | 1 | B | A |
| 312 | 4 | B | C |
| 313 | 1 | A | C |
| 314 | 2 | A | B |
| 315 | 1 | C | B |
| 316 | 3 | A | C |
| 317 | 1 | B | A |
| 318 | 2 | B | C |
| 319 | 1 | A | C |
| 320 | 7 | B | A |
| 321 | 1 | C | B |
| 322 | 2 | C | A |
| 323 | 1 | B | A |
| 324 | 3 | C | B |
| 325 | 1 | A | C |
| 326 | 2 | A | B |
| 327 | 1 | C | B |
| 328 | 4 | C | A |
| 329 | 1 | B | A |
| 330 | 2 | B | C |
| 331 | 1 | A | C |
| 332 | 3 | B | A |
| 333 | 1 | C | B |
| 334 | 2 | C | A |
| 335 | 1 | B | A |
| 336 | 5 | C | B |
| 337 | 1 | A | C |
| 338 | 2 | A | B |
| 339 | 1 | C | B |
| 340 | 3 | A | C |
| 341 | 1 | B | A |
| 342 | 2 | B | C |
| 343 | 1 | A | C |
| 344 | 4 | A | B |
| 345 | 1 | C | B |
| 346 | 2 | C | A |
| 347 | 1 | B | A |
| 348 | 3 | C | B |
| 349 | 1 | A | C |
| 350 | 2 | A | B |
| 351 | 1 | C | B |
| 352 | 6 | C | A |
| 353 | 1 | B | A |
| 354 | 2 | B | C |
| 355 | 1 | A | C |
| 356 | 3 | B | A |
| 357 | 1 | C | B |
| 358 | 2 | C | A |
| 359 | 1 | B | A |
| 360 | 4 | B | C |
| 361 | 1 | A | C |
| 362 | 2 | A | B |
| 363 | 1 | C | B |
| 364 | 3 | A | C |
| 365 | 1 | B | A |
| 366 | 2 | B | C |
| 367 | 1 | A | C |
| 368 | 5 | B | A |
| 369 | 1 | C | B |
| 370 | 2 | C | A |
| 371 | 1 | B | A |
| 372 | 3 | C | B |
| 373 | 1 | A | C |
| 374 | 2 | A | B |
| 375 | 1 | C | B |
| 376 | 4 | C | A |
| 377 | 1 | B | A |
| 378 | 2 | B | C |
| 379 | 1 | A | C |
| 380 | 3 | B | A |
| 381 | 1 | C | B |
| 382 | 2 | C | A |
| 383 | 1 | B | A |
| 384 | 8 | B | C |
| 385 | 1 | A | C |
| 386 | 2 | A | B |
| 387 | 1 | C | B |
| 388 | 3 | A | C |
| 389 | 1 | B | A |
| 390 | 2 | B | C |
| 391 | 1 | A | C |
| 392 | 4 | A | B |
| 393 | 1 | C | B |
| 394 | 2 | C | A |
| 395 | 1 | B | A |
| 396 | 3 | C | B |
| 397 | 1 | A | C |
| 398 | 2 | A | B |
| 399 | 1 | C | B |
| 400 | 5 | A | C |
| 401 | 1 | B | A |
| 402 | 2 | B | C |
| 403 | 1 | A | C |
| 404 | 3 | B | A |
| 405 | 1 | C | B |
| 406 | 2 | C | A |
| 407 | 1 | B | A |
| 408 | 4 | B | C |
| 409 | 1 | A | C |
| 410 | 2 | A | B |
| 411 | 1 | C | B |
| 412 | 3 | A | C |
| 413 | 1 | B | A |
| 414 | 2 | B | C |
| 415 | 1 | A | C |
| 416 | 6 | A | B |
| 417 | 1 | C | B |
| 418 | 2 | C | A |
| 419 | 1 | B | A |
| 420 | 3 | C | B |
| 421 | 1 | A | C |
| 422 | 2 | A | B |
| 423 | 1 | C | B |
| 424 | 4 | C | A |
| 425 | 1 | B | A |
| 426 | 2 | B | C |
| 427 | 1 | A | C |
| 428 | 3 | B | A |
| 429 | 1 | C | B |
| 430 | 2 | C | A |
| 431 | 1 | B | A |
| 432 | 5 | C | B |
| 433 | 1 | A | C |
| 434 | 2 | A | B |
| 435 | 1 | C | B |
| 436 | 3 | A | C |
| 437 | 1 | B | A |
| 438 | 2 | B | C |
| 439 | 1 | A | C |
| 440 | 4 | A | B |
| 441 | 1 | C | B |
| 442 | 2 | C | A |
| 443 | 1 | B | A |
| 444 | 3 | C | B |
| 445 | 1 | A | C |
| 446 | 2 | A | B |
| 447 | 1 | C | B |
| 448 | 7 | A | C |
| 449 | 1 | B | A |
| 450 | 2 | B | C |
| 451 | 1 | A | C |
| 452 | 3 | B | A |
| 453 | 1 | C | B |
| 454 | 2 | C | A |
| 455 | 1 | B | A |
| 456 | 4 | B | C |
| 457 | 1 | A | C |
| 458 | 2 | A | B |
| 459 | 1 | C | B |
| 460 | 3 | A | C |
| 461 | 1 | B | A |
| 462 | 2 | B | C |
| 463 | 1 | A | C |
| 464 | 5 | B | A |
| 465 | 1 | C | B |
| 466 | 2 | C | A |
| 467 | 1 | B | A |
| 468 | 3 | C | B |
| 469 | 1 | A | C |
| 470 | 2 | A | B |
| 471 | 1 | C | B |
| 472 | 4 | C | A |
| 473 | 1 | B | A |
| 474 | 2 | B | C |
| 475 | 1 | A | C |
| 476 | 3 | B | A |
| 477 | 1 | C | B |
| 478 | 2 | C | A |
| 479 | 1 | B | A |
| 480 | 6 | B | C |
| 481 | 1 | A | C |
| 482 | 2 | A | B |
| 483 | 1 | C | B |
| 484 | 3 | A | C |
| 485 | 1 | B | A |
| 486 | 2 | B | C |
| 487 | 1 | A | C |
| 488 | 4 | A | B |
| 489 | 1 | C | B |
| 490 | 2 | C | A |
| 491 | 1 | B | A |
| 492 | 3 | C | B |
| 493 | 1 | A | C |
| 494 | 2 | A | B |
| 495 | 1 | C | B |
| 496 | 5 | A | C |
| 497 | 1 | B | A |
| 498 | 2 | B | C |
| 499 | 1 | A | C |
| 500 | 3 | B | A |
| 501 | 1 | C | B |
| 502 | 2 | C | A |
| 503 | 1 | B | A |
| 504 | 4 | B | C |
| 505 | 1 | A | C |
| 506 | 2 | A | B |
| 507 | 1 | C | B |
| 508 | 3 | A | C |
| 509 | 1 | B | A |
| 510 | 2 | B | C |
| 511 | 1 | A | C |
On this page
The shape of the solution
There are never 511 separate moves to remember — only three stages:
- Moves 1 to 255: build a tower of 8 disks on B.
- Move 256: disk 9 crosses to C — the only time it moves.
- Moves 257 to 511: rebuild the 8-disk tower on top of it.
Stages 1 and 3 are each the 8-disk solution, with two towers' names swapped.
Which disk moves when
Disk 1 makes half of all the moves — 256 of them, on every odd-numbered move. Each larger disk moves half as often as the one above it, which is the binary counter hiding inside the puzzle: the disk that moves is one more than the number of times you can halve the move number and still get a whole number. Move 6 halves once, to 3, so move 6 is disk 2. There is more on that in Tower of Hanoi and binary.
| Disk | Moves | First moves on | Then every |
|---|---|---|---|
| 1 | 256 | move 1 | 2 moves |
| 2 | 128 | move 2 | 4 moves |
| 3 | 64 | move 4 | 8 moves |
| 4 | 32 | move 8 | 16 moves |
| 5 | 16 | move 16 | 32 moves |
| 6 | 8 | move 32 | 64 moves |
| 7 | 4 | move 64 | 128 moves |
| 8 | 2 | move 128 | 256 moves |
| 9 | 1 | move 256 | — |
The smallest disk's circuit
With 9 disks — an odd number — disk 1 travels A → C → B → A for the whole game, never reversing. Every move in between is the only legal move that leaves disk 1 alone. Those two rules alone reproduce the list above move for move; the iterative solution explains why, and strategies turns it into something to play by.
About the 9-disk puzzle
Nine disks can be arranged on three towers in 19,683 different ways — 3⁹, because each disk can sit on any tower and the order on a tower is forced by the rule. Every one of those arrangements is a legal position you could reach. The perfect game passes through just 512 of them, the start and the finish included: about 2.6%.
That is what makes nine disks feel different from the small sizes. At three disks, the 8 positions on the shortest path are nearly a third of everything possible, and a wrong move lands somewhere familiar. At nine, a single slip puts you among the 97% of positions the solution never visits, and finding the way back by eye is genuinely hard. The solver exists for exactly that moment: tell it where the disks are and it finds the shortest route home from any of the 19,683.
Nine is odd, so disk 1 goes to C first. The 511 moves factor as 7 × 73; the game is Expert on this board and runs about eight and a half minutes at a move a second.
Other sizes
- 8 disks255 moves — the solution that makes up each half of this one.
- 10 disks1,023 moves — this solution twice, with one move between.
- Solve 9 disks from a position you are stuck inThe solver finishes a half-played game in the fewest moves left, rather than starting again.
- Every solution, from 3 to 10 disksMove counts, first moves and timings side by side.
Frequently asked questions
How many moves does it take to solve Tower of Hanoi with 9 disks?
511 moves is the minimum: 2⁹ − 1 = 511. No solution with fewer moves exists, and any solution with more has wasted some.
What is the first move in 9-disk Tower of Hanoi?
Move disk 1, the smallest, from tower A to tower C. With an odd number of disks the smallest disk travels A → C → B → A for the whole game, so its first stop is C. Sending it to B first still lets you finish, but it costs one extra move.
How long does 9-disk Tower of Hanoi take to solve?
A perfect game is 511 moves, which at one move a second is 8 minutes and at three moves a second — about as fast as anyone plays by hand — 2 minutes.
How many positions are there in 9-disk Tower of Hanoi?
19,683, which is 3⁹. Each of the nine disks can be on any of the three towers, and once you know which disks share a tower their order is forced, so every one of those arrangements is a legal position. The shortest solution passes through only 512 of them.