| | Number of Real Solutions |
| Necklaces |
1 | 3 |
| Acbbbaa |
0 | 25000 |
| Aacabbb |
927 | 24073 |
| Acabbba |
2427 | 22573 |
| Aacbbba |
2509 | 22491 |
| Acbbaba |
4385 | 20615 |
| Aabbcab |
4501 | 20499 |
| Acbbaab |
5130 | 19870 |
| Acaabbb |
6026 | 18974 |
| Aacbbab |
6776 | 18224 |
| Aabacbb |
6958 | 18042 |
| Abcbaab |
8052 | 16948 |
| Aaabbcb |
8103 | 16897 |
| Aabcbba |
8401 | 16599 |
| Aabcabb |
8534 | 16466 |
| Aaacbbb |
8810 | 16190 |
| Aaabcbb |
9287 | 15713 |
| Aabbacb |
9355 | 15645 |
| Abcabab |
9589 | 15411 |
| Aababcb |
9697 | 15303 |
| Acbaabb |
11085 | 13915 |
| Acbabba |
11372 | 13628 |
| Aabcbab |
13018 | 11982 |
| Abacbab |
13125 | 11875 |
| Acababb |
13223 | 11777 |
| Abaacbb |
13264 | 11736 |
| Abcaabb |
13511 | 11489 |
| Aacbabb |
13525 | 11475 |
| Acbabab |
14647 | 10353 |
| Abacabb |
14735 | 10265 |
| Acabbab |
15028 | 9972 |
|