| | Number of Real Solutions |
| Necklaces |
1 | 3 |
| Aacbbbc |
0 | 25000 |
| Aabbbcc |
0 | 25000 |
| Aabcbbc |
543 | 24457 |
| Accabbb |
936 | 24064 |
| Aabcbcb |
2260 | 22740 |
| Acabbbc |
2835 | 22165 |
| Aabbcbc |
3380 | 21620 |
| Accbbab |
4006 | 20994 |
| Aaccbbb |
4087 | 20913 |
| Acbcbab |
4684 | 20316 |
| Aacbbcb |
5313 | 19687 |
| Acacbbb |
6072 | 18928 |
| Abaccbb |
6158 | 18842 |
| Abccabb |
6289 | 18711 |
| Aabccbb |
6398 | 18602 |
| Acbbcab |
7035 | 17965 |
| Aacbcbb |
8080 | 16920 |
| Aabbccb |
8429 | 16571 |
| Acabcbb |
9217 | 15783 |
| Abcacbb |
9755 | 15245 |
| Abacbcb |
9786 | 15214 |
| Abcabcb |
11421 | 13579 |
| Accbabb |
11495 | 13505 |
| Acbabbc |
11649 | 13351 |
| Acabbcb |
12390 | 12610 |
| Ababccb |
12712 | 12288 |
| Acbcabb |
12896 | 12104 |
| Acbacbb |
13452 | 11548 |
| Acbbacb |
15473 | 9527 |
| Acbabcb |
16628 | 8372 |
|