| | Number of Real Solutions |
| Necklaces |
1 | 3 |
| Addcba |
0 | 25000 |
| Addacb |
0 | 25000 |
| Addbca |
0 | 25000 |
| Aaddcb |
0 | 25000 |
| Aacddb |
97 | 24903 |
| Aadcdb |
173 | 24827 |
| Acaddb |
1225 | 23775 |
| Acdadb |
1406 | 23594 |
| Acddab |
2168 | 22832 |
| Adbcda |
2188 | 22812 |
| Adcbda |
2498 | 22502 |
| Acbdda |
2709 | 22291 |
| Acabdd |
3044 | 21956 |
| Adadcb |
3461 | 21539 |
| Acdbda |
4063 | 20937 |
| Adcadb |
5539 | 19461 |
| Adbdca |
5557 | 19443 |
| Adcdba |
5740 | 19260 |
| Acddba |
6612 | 18388 |
| Addcab |
6666 | 18334 |
| Adcabd |
7035 | 17965 |
| Acbadd |
7286 | 17714 |
| Adcdab |
7448 | 17552 |
| Adacdb |
7776 | 17224 |
| Adacbd |
8214 | 16786 |
| Acdabd |
10995 | 14005 |
| Acadbd |
12026 | 12974 |
| Adcbad |
12201 | 12799 |
| Acdbad |
14209 | 10791 |
| Acbdad |
14340 | 10660 |
|