| | Number of Real Solutions |
| Necklaces |
1 | 3 |
| Aacbbd |
0 | 25000 |
| Aabcbd |
0 | 25000 |
| Aabbcd |
0 | 25000 |
| Acabbd |
3360 | 21640 |
| Adacbb |
3417 | 21583 |
| Acbdab |
3670 | 21330 |
| Acbbad |
4461 | 20539 |
| Acabdb |
4511 | 20489 |
| Adabcb |
4897 | 20103 |
| Acbadb |
5022 | 19978 |
| Aacbdb |
5589 | 19411 |
| Adcabb |
5835 | 19165 |
| Acdbba |
5863 | 19137 |
| Acdabb |
6513 | 18487 |
| Adbacb |
6709 | 18291 |
| Aabcdb |
6969 | 18031 |
| Acbdba |
7334 | 17666 |
| Adbcab |
7492 | 17508 |
| Acdbab |
8684 | 16316 |
| Aadcbb |
9517 | 15483 |
| Adcbab |
10194 | 14806 |
| Aabdcb |
10258 | 14742 |
| Abacdb |
10345 | 14655 |
| Acbabd |
10488 | 14512 |
| Aacdbb |
10492 | 14508 |
| Abcadb |
11006 | 13994 |
| Abcdab |
11077 | 13923 |
| Acadbb |
11289 | 13711 |
| Aadbcb |
11907 | 13093 |
| Acbbda |
11967 | 13033 |
|