| | Number of Real Solutions |
| Necklaces |
0 |
2 | 4 | 6 | 8 |
| bbbaddc |
0 | 0 | 0 | 0 |
2500 |
| bbbadcd |
0 | 0 | 0 | 0 |
2500 |
| bbbacdd |
0 | 0 | 0 | 0 |
2500 |
| bbabddc |
0 | 0 | 0 | 0 |
2500 |
| bbabdcd |
0 | 0 | 0 | 0 |
2500 |
| bbabcdd |
0 | 0 | 0 | 0 |
2500 |
| bbdabdc |
0 | 0 | 10 | 1350 |
1140 |
| bbacdbd |
0 | 0 | 20 | 740 |
1740 |
| bbdbacd |
0 | 0 | 21 | 1179 |
1300 |
| bbdabcd |
0 | 0 | 24 | 1440 |
1036 |
| bbdbadc |
0 | 0 | 35 | 1358 |
1107 |
| babdbdc |
0 | 0 | 41 | 892 |
1567 |
| bbadbdc |
0 | 0 | 66 | 607 |
1827 |
| bbadcbd |
0 | 0 | 170 | 899 |
1431 |
| bbadbcd |
0 | 0 | 178 | 816 |
1506 |
| bbacbdd |
0 | 0 | 181 | 1216 |
1103 |
| babdbcd |
0 | 0 | 212 | 1009 |
1279 |
| bbddbac |
0 | 0 | 271 | 1431 |
798 |
| bbaddbc |
0 | 0 | 318 | 1134 |
1048 |
| bbddabc |
0 | 0 | 405 | 1146 |
949 |
| babddbc |
0 | 0 | 483 | 1217 |
800 |
| badbcbd |
0 | 0 | 682 | 1195 |
623 |
| bbbdacd |
0 | 1 | 58 | 570 |
1871 |
| bbdbcad |
0 | 1 | 703 | 1082 |
714 |
| bacbdbd |
0 | 1 | 749 | 1285 |
465 |
| badbdbc |
0 | 2 | 725 | 1312 |
461 |
| bbdbdac |
0 | 28 | 380 | 1250 |
842 |
| bbbdadc |
0 | 72 | 299 | 1022 |
1107 |
| bbbddac |
0 | 108 | 486 | 733 |
1173 |
| bbdadbc |
0 | 113 | 700 | 1160 |
527 |
|