| | Number of Real Solutions |
| Necklaces |
1 | 3 |
| Aabbcc |
0 | 25000 |
| Abaccb |
3372 | 21628 |
| Accbab |
3972 | 21028 |
| Aacbbc |
4498 | 20502 |
| Aaccbb |
6565 | 18435 |
| Acabbc |
6594 | 18406 |
| Abcacb |
7132 | 17868 |
| Aabccb |
8449 | 16551 |
| Accabb |
8880 | 16120 |
| Aacbcb |
9240 | 15760 |
| Acabcb |
9804 | 15196 |
| Acbabc |
10850 | 14150 |
| Acbcab |
11866 | 13134 |
| Aabcbc |
11870 | 13130 |
| Acacbb |
12699 | 12301 |
| Acbacb |
13342 | 11658 |
|