| | Number of Real Solutions |
| Necklaces |
1 | 3 |
| Abacdd |
0 | 25000 |
| Addbac |
0 | 25000 |
| Addabc |
0 | 25000 |
| Addcba |
0 | 25000 |
| Addbca |
815 | 24185 |
| Adbcad |
1903 | 23097 |
| Abaddc |
2057 | 22943 |
| Adadbc |
2264 | 22736 |
| Adabcd |
2412 | 22588 |
| Aabddc |
2546 | 22454 |
| Adbacd |
2894 | 22106 |
| Adbdac |
3660 | 21340 |
| Adabdc |
3949 | 21051 |
| Abcadd |
5060 | 19940 |
| Adbadc |
5510 | 19490 |
| Abcdda |
5643 | 19357 |
| Adcbda |
5756 | 19244 |
| Adbcda |
6547 | 18453 |
| Abdadc |
6760 | 18240 |
| Aaddbc |
7375 | 17625 |
| Abcdad |
7409 | 17591 |
| Abddca |
8582 | 16418 |
| Abdcad |
9486 | 15514 |
| Aadbdc |
10090 | 14910 |
| Abdacd |
11082 | 13918 |
| Abadcd |
11293 | 13707 |
| Adbdca |
11599 | 13401 |
| Adcdba |
12047 | 12953 |
| Abdcda |
13658 | 11342 |
| Abddac |
14027 | 10973 |
|