| | Number of Real Solutions |
| Necklaces |
1 | 3 |
| Adccba |
0 | 25000 |
| Acdcba |
0 | 25000 |
| Accdba |
0 | 25000 |
| Aadccb |
0 | 25000 |
| Aacdcb |
0 | 25000 |
| Aaccdb |
0 | 25000 |
| Acdbac |
4108 | 20892 |
| Acacdb |
4399 | 20601 |
| Adbcca |
4411 | 20589 |
| Accbda |
4617 | 20383 |
| Acbcda |
5070 | 19930 |
| Acadbc |
5314 | 19686 |
| Acdcab |
5509 | 19491 |
| Adbcac |
5919 | 19081 |
| Adaccb |
6138 | 18862 |
| Acbdca |
6245 | 18755 |
| Acadcb |
6604 | 18396 |
| Adccab |
7029 | 17971 |
| Acdbca |
7646 | 17353 |
| Accdab |
7985 | 17015 |
| Acdacb |
8788 | 16212 |
| Accadb |
8836 | 16164 |
| Adcabc |
9798 | 15202 |
| Adcbca |
9949 | 15051 |
| Adabcc |
10501 | 14499 |
| Adcacb |
10708 | 14292 |
| Adbacc |
10932 | 14068 |
| Adacbc |
11563 | 13437 |
| Acdabc |
11593 | 13407 |
| Adcbac |
12461 | 12539 |
|