| | Number of Real Solutions |
| Necklaces |
0 |
2 | 4 |
| abcdef |
0 | 0 | 25000 |
| aedfbc |
0 | 0 | 25000 |
| acedfb |
0 | 0 | 25000 |
| adfebc |
0 | 0 | 25000 |
| acdfeb |
0 | 0 | 25000 |
| adfecb |
0 | 0 | 25000 |
| abdfec |
0 | 0 | 25000 |
| abcdfe |
0 | 0 | 25000 |
| acbdfe |
0 | 0 | 25000 |
| aedfcb |
0 | 0 | 25000 |
| abedfc |
0 | 0 | 25000 |
| abcedf |
0 | 0 | 25000 |
| acbedf |
0 | 0 | 25000 |
| afedbc |
0 | 0 | 25000 |
| acfedb |
0 | 0 | 25000 |
| adefbc |
0 | 0 | 25000 |
| acdefb |
0 | 0 | 25000 |
| adefcb |
0 | 0 | 25000 |
| abdfce |
0 | 603 | 24397 |
| adfceb |
0 | 718 | 24282 |
| abecdf |
0 | 750 | 24250 |
| aecdfb |
0 | 803 | 24197 |
| aebcdf |
0 | 5376 | 19624 |
| aecbdf |
0 | 5463 | 19537 |
| abfcde |
0 | 5573 | 19427 |
| adfbec |
0 | 5585 | 19415 |
| aebdfc |
0 | 5612 | 19388 |
| adfbce |
0 | 5719 | 19281 |
| acdfbe |
0 | 5753 | 19247 |
| afecdb |
0 | 5775 | 19225 |
| adecfb |
0 | 5775 | 19225 |
| afcedb |
0 | 5787 | 19213 |
| adcefb |
0 | 5787 | 19213 |
| acebdf |
0 | 5801 | 19199 |
| adfcbe |
0 | 5871 | 19129 |
| afcdeb |
0 | 5924 | 19076 |
| adcfeb |
0 | 5924 | 19076 |
| aefcdb |
0 | 5950 | 19050 |
| adcbef |
0 | 12290 | 12710 |
| adbcfe |
0 | 12333 | 12667 |
| afbcde |
0 | 12333 | 12667 |
| acdbfe |
0 | 12437 | 12563 |
| adbefc |
0 | 12611 | 12389 |
| adebcf |
0 | 12720 | 12280 |
| acdebf |
0 | 12759 | 12241 |
| aedbfc |
0 | 12762 | 12238 |
| afcdbe |
30 | 5295 | 19675 |
| adcfbe |
30 | 5295 | 19675 |
| acdbef |
789 | 6514 | 17697 |
| adebfc |
812 | 5887 | 18301 |
| adcbfe |
813 | 6073 | 18114 |
| aedbcf |
838 | 6222 | 17940 |
| acedbf |
1441 | 7029 | 16530 |
| adecbf |
1456 | 6762 | 16782 |
| adbfec |
1486 | 6608 | 16906 |
| adbcef |
1487 | 6503 | 17010 |
| adbecf |
4336 | 7918 | 12746 |
| adcebf |
4337 | 7960 | 12703 |
| aecdbf |
4377 | 8383 | 12240 |
| adbfce |
4420 | 7653 | 12927 |
| |
| Projections |
| Variety | Problem | # |
| Fl(2,3;5) |
(X )2X (Y )2Y
| 4 |
| Fl(1,2,3;5) |
W X X (Y )2Y
| |
| Fl(2,3,4;5) |
(X )2X Y Y Z
| |
|
|