| | Number of Real Solutions |
| Necklaces |
1 | 3 |
| Adcbba |
0 | 25000 |
| Adbcba |
0 | 25000 |
| Adbbca |
0 | 25000 |
| Aadbcb |
1672 | 23328 |
| Aadcbb |
1703 | 23297 |
| Acabbd |
2024 | 22976 |
| Acbbda |
2657 | 22343 |
| Abcadb |
4247 | 20753 |
| Acdbba |
4781 | 20219 |
| Aacbdb |
5334 | 19662 |
| Adcabb |
5999 | 19001 |
| Abcdab |
6384 | 18616 |
| Adbacb |
6554 | 18446 |
| Aabcdb |
6565 | 18435 |
| Acbabd |
7186 | 17814 |
| Abdcab |
7251 | 17749 |
| Acadbb |
7594 | 17406 |
| Aacdbb |
7676 | 17324 |
| Adbcab |
7700 | 17300 |
| Acbadb |
7922 | 17078 |
| Adacbb |
8251 | 16749 |
| Acbbad |
8338 | 16662 |
| Adcbab |
9086 | 15914 |
| Acbdba |
9372 | 15622 |
| Acdabb |
9642 | 15358 |
| Aabdcb |
9820 | 15180 |
| Adabcb |
9930 | 15070 |
| Acabdb |
11185 | 13811 |
| Acdbab |
11816 | 13184 |
| Acbdab |
14977 | 10023 |
|