| | Number of Real Solutions |
| Necklaces |
1 | 3 |
| Acbdda |
0 | 25000 |
| Addcba |
0 | 25000 |
| Addbca |
0 | 25000 |
| Adacbd |
0 | 25000 |
| Aaddcb |
0 | 25000 |
| Adcbad |
734 | 24266 |
| Addacb |
774 | 24226 |
| Acddba |
846 | 24154 |
| Addcab |
944 | 24056 |
| Adadcb |
1529 | 23471 |
| Adcdab |
1719 | 23281 |
| Acbdad |
1825 | 23175 |
| Adbcda |
2296 | 22704 |
| Aadcdb |
3729 | 21271 |
| Adcabd |
4557 | 20443 |
| Acddab |
4844 | 20156 |
| Acabdd |
5661 | 19339 |
| Adacdb |
5777 | 19223 |
| Aacddb |
5971 | 19029 |
| Acdabd |
6494 | 18506 |
| Acadbd |
6560 | 18440 |
| Adcdba |
6565 | 18435 |
| Adcadb |
6666 | 18334 |
| Acdbad |
7490 | 17510 |
| Acbadd |
7594 | 17406 |
| Adcbda |
8284 | 16716 |
| Acaddb |
8635 | 16365 |
| Acdadb |
9457 | 15543 |
| Acdbda |
10187 | 14813 |
| Adbdca |
13068 | 11932 |
|