| | Number of Real Solutions |
| Necklaces |
1 | 3 |
| Adcbba |
0 | 25000 |
| Acdbba |
0 | 25000 |
| Aadcbb |
0 | 25000 |
| Aacdbb |
0 | 25000 |
| Abdcab |
111 | 24889 |
| Acadbb |
621 | 24379 |
| Acabdb |
631 | 24369 |
| Acbbda |
1107 | 23893 |
| Adbbac |
1508 | 23492 |
| Abcdab |
1623 | 23377 |
| Aabcdb |
1637 | 23363 |
| Adbcab |
1907 | 23093 |
| Adacbb |
2574 | 22426 |
| Adabbc |
3904 | 21096 |
| Aacbdb |
4242 | 20758 |
| Acdbab |
4828 | 20172 |
| Acbdba |
4901 | 20099 |
| Abdacb |
5264 | 19736 |
| Acbdab |
5394 | 19606 |
| Aabdcb |
5506 | 19494 |
| Adcbab |
5604 | 19396 |
| Adbacb |
5659 | 19341 |
| Acdabb |
6320 | 18680 |
| Adbbca |
9091 | 15909 |
| Acbadb |
9353 | 15647 |
| Adcabb |
9367 | 15633 |
| Adabcb |
10361 | 14639 |
| Aadbcb |
10586 | 14414 |
| Adbabc |
11310 | 13690 |
| Adbcba |
12837 | 12163 |
|