| | Number of Real Solutions |
| Necklaces |
0 |
2 | 4 | 6 |
| Abaadc |
0 | 0 | 0 | 10000 |
| Abaacd |
0 | 0 | 0 | 10000 |
| Aabadc |
0 | 0 | 0 | 10000 |
| Aabacd |
0 | 0 | 0 | 10000 |
| Aaabdc |
0 | 0 | 0 | 10000 |
| Aaabcd |
0 | 0 | 0 | 10000 |
| Aaadbc |
0 | 0 | 0 | 10000 |
| Adaabc |
0 | 0 | 1057 | 8943 |
| Aadabc |
0 | 4 | 1258 | 8738 |
| Aabcda |
0 | 6 | 1085 | 8909 |
| Abacda |
0 | 17 | 1610 | 8373 |
| Abcdaa |
0 | 25 | 2054 | 7921 |
| Adbaac |
0 | 40 | 1512 | 8448 |
| Abdcaa |
0 | 52 | 3054 | 6894 |
| Aacabd |
0 | 67 | 3798 | 6135 |
| Adabac |
0 | 79 | 1110 | 8811 |
| Aacbad |
0 | 168 | 2638 | 7194 |
| Aadbac |
0 | 307 | 2556 | 7137 |
| Abadca |
0 | 311 | 2133 | 7556 |
| Aabdca |
0 | 443 | 2288 | 7269 |
| Abcaad |
0 | 476 | 5366 | 4158 |
| Abdaac |
0 | 624 | 2510 | 6866 |
| Abadac |
0 | 1275 | 551 | 8174 |
| Aadbca |
0 | 1451 | 421 | 8128 |
| Aabdac |
0 | 1455 | 504 | 8041 |
| Aaacbd |
0 | 1554 | 2167 | 6279 |
| Abdaca |
0 | 2966 | 3474 | 3560 |
| Abacad |
0 | 3673 | 3298 | 3029 |
| Aabcad |
0 | 3719 | 3157 | 3124 |
| Abcada |
0 | 3742 | 3262 | 2996 |
|