Snake-in-the-Box lower bounds
Click on any length in the table to show a sample snake/coil of that type
in the box below, or use the box to validate a snake of your own.
Lengths in dimensions 1‑8 are proven to be maximal.
Please
let me know
of any snake/coil longer than those listed here.
For more info, please see the FAQ.
| dimension | length | ||
|---|---|---|---|
| snake | coil | symmetric coil | |
| 1 | 1 | ||
| 2 | 2 | 4 | 4 |
| 3 | 4 | 6 | 6 |
| 4 | 7 | 8 | 8 |
| 5 | 13 | 14 | 14 |
| 6 | 26 | 26 | 26 |
| 7 | 50 | 48 | 46 |
| 8 | 98 | 96 | 94 |
| 9 | 190 | 188 | 186 |
| 10 | 376 | 370 | 362 |
| 11 | 743 | 728 | 718 |
| 12 | 1465 | 1442 | 1430 |
| 13 | 2900 | 2840 | 2810 |
To validate a snake or coil of your own construction, enter its transition sequence in the box below and click the analyze button.