| | Number of Real Solutions |
| Necklaces |
1 | 3 |
| Aaabbbc |
0 | 25000 |
| Aabbbac |
0 | 25000 |
| Aacbbba |
2310 | 22690 |
| Aaacbbb |
3181 | 21819 |
| Aaabcbb |
3204 | 21796 |
| Aababbc |
4421 | 20579 |
| Abaabcb |
4494 | 20506 |
| Abcaabb |
5329 | 19671 |
| Aabcbba |
5592 | 19408 |
| Acbbaab |
6219 | 18781 |
| Abacabb |
6544 | 18456 |
| Aaabbcb |
6873 | 18127 |
| Acaabbb |
7261 | 17739 |
| Aababcb |
7269 | 17731 |
| Abaacbb |
7474 | 17526 |
| Abacbab |
8382 | 16618 |
| Aacabbb |
8541 | 16459 |
| Aabacbb |
8834 | 16166 |
| Aabbabc |
9257 | 15743 |
| Acababb |
9626 | 15374 |
| Ababacb |
9711 | 15289 |
| Acbaabb |
9751 | 15249 |
| Aabbacb |
12852 | 12148 |
| Acabbab |
12903 | 12097 |
| Aacbbab |
13414 | 11586 |
| Aabcbab |
13757 | 11243 |
| Aabbcab |
14030 | 10970 |
| Acbabab |
14716 | 10284 |
| Aabcabb |
15509 | 9491 |
| Aacbabb |
15808 | 9192 |
|