| | Number of Real Solutions |
| Necklaces |
1 | 3 | 5 |
7 | 9 | 11 | 13 | 15 |
| DCBbAa |
0 | 0 | 0 | 3 |
76 | 71 | 16 | 34 |
| DBAbaC |
0 | 0 | 0 | 5 |
25 | 61 | 58 | 51 |
| DbCAaB |
0 | 0 | 0 | 5 |
36 | 68 | 61 | 30 |
| DBaAbC |
0 | 0 | 0 | 6 |
44 | 72 | 36 | 42 |
| DABbaC |
0 | 0 | 0 | 6 |
54 | 81 | 35 | 24 |
| DBbAaC |
0 | 0 | 0 | 8 |
24 | 32 | 52 | 84 |
| DBbACa |
0 | 0 | 0 | 10 |
38 | 56 | 64 | 32 |
| DBCaAb |
0 | 0 | 0 | 12 |
50 | 72 | 36 | 30 |
| DBaCAb |
0 | 0 | 0 | 13 |
56 | 60 | 43 | 28 |
| DCbBAa |
0 | 0 | 0 | 17 |
73 | 77 | 17 | 16 |
| DBCbAa |
0 | 0 | 0 | 40 |
77 | 45 | 28 | 10 |
| DBbCaA |
0 | 0 | 1 | 6 |
48 | 84 | 50 | 11 |
| DABbCa |
0 | 0 | 1 | 19 |
47 | 71 | 51 | 11 |
| DBAaCb |
0 | 0 | 1 | 21 |
45 | 64 | 43 | 26 |
| DBCAba |
0 | 0 | 1 | 43 |
68 | 57 | 22 | 9 |
| DbBCaA |
0 | 0 | 2 | 14 |
44 | 62 | 52 | 26 |
| DbBaCA |
0 | 0 | 2 | 30 |
62 | 52 | 37 | 17 |
| DCBAba |
0 | 0 | 2 | 38 |
51 | 67 | 14 | 28 |
| DBbaCA |
0 | 0 | 2 | 40 |
67 | 46 | 36 | 9 |
| DBabAC |
0 | 0 | 3 | 11 |
52 | 56 | 51 | 27 |
| DBAabC |
0 | 0 | 3 | 26 |
47 | 67 | 36 | 21 |
| DbABCa |
0 | 0 | 3 | 27 |
79 | 49 | 28 | 14 |
| DBACab |
0 | 0 | 4 | 17 |
60 | 76 | 33 | 10 |
| DAabBC |
0 | 0 | 4 | 19 |
51 | 77 | 38 | 11 |
| DBAbCa |
0 | 0 | 4 | 22 |
32 | 56 | 42 | 44 |
| DbCBaA |
0 | 0 | 4 | 26 |
82 | 39 | 34 | 15 |
| DABCba |
0 | 0 | 4 | 31 |
69 | 61 | 26 | 9 |
| DCAbBa |
0 | 0 | 5 | 16 |
62 | 66 | 42 | 9 |
| DbBAaC |
0 | 0 | 5 | 22 |
27 | 49 | 46 | 51 |
| DBbCAa |
0 | 0 | 5 | 23 |
50 | 53 | 41 | 28 |
| DBCabA |
0 | 0 | 5 | 40 |
63 | 53 | 24 | 15 |
| DbBaAC |
0 | 0 | 6 | 22 |
43 | 76 | 34 | 19 |
| DbABaC |
0 | 0 | 6 | 49 |
39 | 57 | 25 | 24 |
| DCbABa |
0 | 0 | 6 | 50 |
61 | 51 | 22 | 10 |
| DBaCbA |
0 | 0 | 7 | 18 |
44 | 74 | 40 | 17 |
| DBabCA |
0 | 0 | 7 | 31 |
51 | 58 | 29 | 24 |
| DAbCBa |
0 | 0 | 7 | 34 |
75 | 42 | 38 | 4 |
| DbCBAa |
0 | 0 | 8 | 36 |
59 | 54 | 30 | 13 |
| DbaBAC |
0 | 0 | 8 | 40 |
59 | 57 | 26 | 10 |
| DACBba |
0 | 0 | 9 | 42 |
71 | 49 | 18 | 11 |
| DBCAab |
0 | 0 | 11 | 23 |
64 | 47 | 35 | 20 |
| DCABba |
0 | 0 | 11 | 31 |
55 | 64 | 27 | 12 |
| DBCbaA |
0 | 0 | 12 | 41 |
70 | 37 | 29 | 11 |
| DACbBa |
0 | 0 | 14 | 29 |
36 | 62 | 46 | 13 |
| DbACBa |
0 | 0 | 15 | 58 |
42 | 48 | 28 | 9 |
| DAbBaC |
0 | 0 | 16 | 50 |
63 | 38 | 23 | 10 |
| DbCABa |
0 | 0 | 18 | 32 |
50 | 53 | 27 | 20 |
| DAaBbC |
0 | 0 | 18 | 40 |
56 | 45 | 33 | 8 |
| DbBCAa |
0 | 1 | 0 | 28 |
62 | 62 | 33 | 14 |
| DbBACa |
0 | 1 | 7 | 23 |
45 | 66 | 48 | 10 |
| DbaCBA |
0 | 1 | 11 | 46 |
74 | 47 | 16 | 5 |
| DBACba |
0 | 1 | 13 | 28 |
30 | 77 | 38 | 13 |
| DAbaBC |
0 | 1 | 15 | 67 |
48 | 37 | 20 | 12 |
| DAbBCa |
0 | 2 | 18 | 44 |
74 | 36 | 23 | 3 |
| DABabC |
0 | 3 | 27 | 45 |
43 | 39 | 25 | 18 |
| DbAaBC |
0 | 4 | 24 | 42 |
37 | 39 | 36 | 18 |
| DBbaAC |
0 | 5 | 25 | 23 |
43 | 30 | 47 | 27 |
| DbaABC |
0 | 7 | 13 | 42 |
50 | 48 | 23 | 17 |
| DbCaBA |
0 | 7 | 27 | 55 |
44 | 30 | 26 | 11 |
| DbaBCA |
4 | 14 | 18 | 47 |
49 | 35 | 22 | 11 |
|