| | Number of Real Solutions |
| Necklaces |
0 |
2 | 4 | 6 | 8 |
|---|
| cbaaabddd |
0 | 0 | 0 | 0 |
5000 |
|---|
| cdddbbaaa |
0 | 0 | 0 | 0 |
5000 |
|---|
| cbdddbaaa |
0 | 0 | 0 | 0 |
5000 |
|---|
| cbaaadddb |
0 | 0 | 0 | 0 |
5000 |
|---|
| cbbaaaddd |
0 | 0 | 0 | 0 |
5000 |
|---|
| cbbdddaaa |
0 | 0 | 0 | 0 |
5000 |
|---|
| caadaddbb |
0 | 0 | 0 | 584 |
4416 |
|---|
| cddadaabb |
0 | 0 | 0 | 584 |
4416 |
|---|
| cbddadaab |
0 | 0 | 0 | 827 |
4173 |
|---|
| cdaaaddbb |
0 | 0 | 60 | 869 |
4071 |
|---|
| cbbaaddda |
0 | 0 | 105 | 1211 |
3684 |
|---|
| cadddbbaa |
0 | 0 | 280 | 652 |
4068 |
|---|
| cddbbaaad |
0 | 0 | 295 | 670 |
4035 |
|---|
| caadddbba |
0 | 0 | 414 | 1232 |
3354 |
|---|
| cbbaaddad |
0 | 0 | 415 | 2053 |
2532 |
|---|
| cbbddaada |
0 | 0 | 415 | 2053 |
2532 |
|---|
| cddaadabb |
0 | 0 | 420 | 2272 |
2308 |
|---|
| caaddadbb |
0 | 0 | 420 | 2272 |
2308 |
|---|
| cdbbaaadd |
0 | 0 | 456 | 1070 |
3474 |
|---|
| cadddbaab |
0 | 0 | 532 | 1201 |
3267 |
|---|
| cdbddbaaa |
0 | 0 | 581 | 200 |
4219 |
|---|
| cddbbaada |
0 | 0 | 588 | 1596 |
2816 |
|---|
| cdaadadbb |
0 | 0 | 591 | 1329 |
3080 |
|---|
| cabaadddb |
0 | 0 | 657 | 167 |
4176 |
|---|
| cdddbaaba |
0 | 0 | 708 | 288 |
4004 |
|---|
| cdbaaaddb |
0 | 0 | 746 | 1211 |
3043 |
|---|
| cdaddbbaa |
0 | 0 | 748 | 1686 |
2566 |
|---|
| cbdaddaab |
0 | 0 | 757 | 2693 |
1550 |
|---|
| cbadaaddb |
0 | 0 | 757 | 2693 |
1550 |
|---|
| caadddabb |
0 | 0 | 795 | 2573 |
1632 |
|---|
| cddaaadbb |
0 | 0 | 795 | 2573 |
1632 |
|---|
| cbaaaddbd |
0 | 0 | 808 | 210 |
3982 |
|---|
| cbddbaaad |
0 | 0 | 816 | 1542 |
2642 |
|---|
| cddbbadaa |
0 | 0 | 845 | 2147 |
2008 |
|---|
| cadaddabb |
0 | 0 | 936 | 2329 |
1735 |
|---|
| cdbaaabdd |
0 | 0 | 1014 | 311 |
3675 |
|---|
| cabdddbaa |
0 | 0 | 1014 | 311 |
3675 |
|---|
| cadaabddb |
0 | 0 | 1021 | 2001 |
1978 |
|---|
| cdaddbaab |
0 | 0 | 1021 | 2001 |
1978 |
|---|
| caabddadb |
0 | 0 | 1040 | 2593 |
1367 |
|---|
| cddbaadab |
0 | 0 | 1040 | 2593 |
1367 |
|---|
| cdddaabba |
0 | 0 | 1083 | 605 |
3312 |
|---|
| caaaddbbd |
0 | 0 | 1083 | 605 |
3312 |
|---|
| cdadadabb |
0 | 0 | 1093 | 2295 |
1612 |
|---|
| cddadbbaa |
0 | 0 | 1193 | 2189 |
1618 |
|---|
| cbaadddba |
0 | 0 | 1200 | 1435 |
2365 |
|---|
| cbbdaadad |
0 | 0 | 1234 | 2484 |
1282 |
|---|
| cbadddaab |
0 | 0 | 1276 | 2348 |
1376 |
|---|
| cbdaaaddb |
0 | 0 | 1276 | 2348 |
1376 |
|---|
| cddbaaadb |
0 | 0 | 1289 | 1834 |
1877 |
|---|
| caabdaddb |
0 | 0 | 1374 | 2346 |
1280 |
|---|
| cbbdadada |
0 | 0 | 1397 | 2326 |
1277 |
|---|
| cbadddbaa |
0 | 0 | 1591 | 1907 |
1502 |
|---|
| cddbbdaaa |
0 | 0 | 1630 | 1960 |
1410 |
|---|
| cbaaadbdd |
0 | 0 | 1676 | 861 |
2463 |
|---|
| cbdddabaa |
0 | 0 | 1676 | 861 |
2463 |
|---|
| cbaadabdd |
0 | 0 | 1678 | 2273 |
1049 |
|---|
| cddbdbaaa |
0 | 0 | 1688 | 802 |
2510 |
|---|
| cbdbaadad |
0 | 0 | 1784 | 2342 |
874 |
|---|
| cdddabbaa |
0 | 0 | 1816 | 1942 |
1242 |
|---|
| cddadbaab |
0 | 0 | 1874 | 2365 |
761 |
|---|
| caadabddb |
0 | 0 | 1874 | 2365 |
761 |
|---|
| cdddbabaa |
0 | 0 | 1881 | 862 |
2257 |
|---|
| cdddaabab |
0 | 0 | 2010 | 410 |
2580 |
|---|
| caaaddbdb |
0 | 0 | 2010 | 410 |
2580 |
|---|
| caadddbab |
0 | 0 | 2067 | 1522 |
1411 |
|---|
| cdddabaab |
0 | 0 | 2086 | 916 |
1998 |
|---|
| cbddbdaaa |
0 | 0 | 2107 | 922 |
1971 |
|---|
| cbdbaaadd |
0 | 0 | 2306 | 1459 |
1235 |
|---|
| cbdadadab |
0 | 0 | 2666 | 1746 |
588 |
|---|
| cadaddbab |
0 | 1 | 1456 | 2496 |
1047 |
|---|
| cbbdaadda |
0 | 2 | 434 | 2421 |
2143 |
|---|
| cbbaddaad |
0 | 2 | 434 | 2421 |
2143 |
|---|
| cbbadadda |
0 | 2 | 764 | 1706 |
2528 |
|---|
| cbdaaddab |
0 | 8 | 1489 | 2270 |
1233 |
|---|
| cdbbaadad |
0 | 9 | 447 | 1291 |
3253 |
|---|
| cabbddada |
0 | 9 | 447 | 1291 |
3253 |
|---|
| cbadaddba |
0 | 10 | 1598 | 1703 |
1689 |
|---|
| cdbaadadb |
0 | 13 | 1173 | 1547 |
2267 |
|---|
| cbaadadbd |
0 | 14 | 813 | 1396 |
2777 |
|---|
| cbddadaba |
0 | 14 | 813 | 1396 |
2777 |
|---|
| cdaaddbba |
0 | 16 | 362 | 1659 |
2963 |
|---|
| cdbbaadda |
0 | 17 | 311 | 1318 |
3354 |
|---|
| cadddabab |
0 | 23 | 2061 | 1304 |
1612 |
|---|
| cdaaadbdb |
0 | 23 | 2061 | 1304 |
1612 |
|---|
| cbddabdaa |
0 | 26 | 1280 | 2438 |
1256 |
|---|
| cbaadbadd |
0 | 26 | 1280 | 2438 |
1256 |
|---|
| cbabdadda |
0 | 30 | 1827 | 2309 |
834 |
|---|
| cbdbadaad |
0 | 30 | 1827 | 2309 |
834 |
|---|
| cdabddaab |
0 | 31 | 1092 | 2447 |
1430 |
|---|
| cadbaaddb |
0 | 31 | 1092 | 2447 |
1430 |
|---|
| cbaddadba |
0 | 32 | 1830 | 2291 |
847 |
|---|
| cadadbdab |
0 | 34 | 1924 | 2313 |
729 |
|---|
| cdadabadb |
0 | 34 | 1924 | 2313 |
729 |
|---|
| cbaddadab |
0 | 34 | 2311 | 1939 |
716 |
|---|
| cbdaadadb |
0 | 34 | 2311 | 1939 |
716 |
|---|
| caddabadb |
0 | 39 | 1678 | 2459 |
824 |
|---|
| cdbadaadb |
0 | 41 | 1424 | 2441 |
1094 |
|---|
| cadbadadb |
0 | 43 | 1855 | 2173 |
929 |
|---|
| cbaddabad |
0 | 43 | 2778 | 1480 |
699 |
|---|
| cbadbdaad |
0 | 44 | 1856 | 2311 |
789 |
|---|
| cadbdaadb |
0 | 45 | 2703 | 1498 |
754 |
|---|
| cbdabaadd |
0 | 48 | 2143 | 1784 |
1025 |
|---|
| cbadbddaa |
0 | 48 | 2143 | 1784 |
1025 |
|---|
| cbadadbad |
0 | 49 | 2115 | 2139 |
697 |
|---|
| cadadbadb |
0 | 49 | 2409 | 2052 |
490 |
|---|
| cbaddbaad |
0 | 50 | 1453 | 2310 |
1187 |
|---|
| caddadbba |
0 | 53 | 277 | 1835 |
2835 |
|---|
| caddbaadb |
0 | 53 | 1368 | 2253 |
1326 |
|---|
| cdbdaadab |
0 | 54 | 1050 | 2731 |
1165 |
|---|
| cabaddadb |
0 | 54 | 1050 | 2731 |
1165 |
|---|
| cdbaaddba |
0 | 58 | 553 | 2009 |
2380 |
|---|
| cdbbadaad |
0 | 60 | 282 | 1991 |
2667 |
|---|
| caddbbaad |
0 | 62 | 537 | 922 |
3479 |
|---|
| cadbdadab |
0 | 63 | 1612 | 2108 |
1217 |
|---|
| cdabadadb |
0 | 63 | 1612 | 2108 |
1217 |
|---|
| cddabaabd |
0 | 65 | 2103 | 1059 |
1773 |
|---|
| caadbddba |
0 | 65 | 2103 | 1059 |
1773 |
|---|
| cbadbadad |
0 | 68 | 2332 | 2168 |
432 |
|---|
| cdbbadada |
0 | 70 | 685 | 2188 |
2057 |
|---|
| cdadadbba |
0 | 76 | 708 | 2443 |
1773 |
|---|
| cadbddaab |
0 | 77 | 1297 | 1748 |
1878 |
|---|
| caadadbdb |
0 | 82 | 2017 | 1546 |
1355 |
|---|
| cadbbaadd |
0 | 84 | 993 | 2116 |
1807 |
|---|
| cdbaabdad |
0 | 86 | 1533 | 2291 |
1090 |
|---|
| cadbbadad |
0 | 87 | 1069 | 2296 |
1548 |
|---|
| cadabddba |
0 | 93 | 1358 | 2145 |
1404 |
|---|
| cddabadba |
0 | 94 | 1732 | 2367 |
807 |
|---|
| caadbdabd |
0 | 94 | 1732 | 2367 |
807 |
|---|
| cadadbbad |
0 | 95 | 1125 | 2228 |
1552 |
|---|
| cbabadadd |
0 | 95 | 1880 | 1490 |
1535 |
|---|
| cabbadadd |
0 | 98 | 734 | 866 |
3302 |
|---|
| caaddbbad |
0 | 100 | 904 | 2125 |
1871 |
|---|
| cbddaabad |
0 | 105 | 1468 | 2053 |
1374 |
|---|
| cdadbdaab |
0 | 109 | 2133 | 1949 |
809 |
|---|
| cadabaddb |
0 | 109 | 2133 | 1949 |
809 |
|---|
| cdbaadbad |
0 | 112 | 975 | 2432 |
1481 |
|---|
| cadbaddba |
0 | 117 | 917 | 2347 |
1619 |
|---|
| cabddbaad |
0 | 118 | 817 | 1614 |
2451 |
|---|
| cdbaabdda |
0 | 118 | 817 | 1614 |
2451 |
|---|
| cabbaddad |
0 | 119 | 1004 | 1814 |
2063 |
|---|
| cdadbaadb |
0 | 119 | 1814 | 2030 |
1037 |
|---|
| cdadbbaad |
0 | 121 | 1215 | 2173 |
1491 |
|---|
| caadadbbd |
0 | 127 | 920 | 1086 |
2867 |
|---|
| cdbdbadaa |
0 | 127 | 1452 | 2341 |
1080 |
|---|
| cababdadd |
0 | 127 | 1452 | 2341 |
1080 |
|---|
| cbdadbdaa |
0 | 136 | 2453 | 1764 |
647 |
|---|
| cbadabadd |
0 | 136 | 2453 | 1764 |
647 |
|---|
| cbadbaadd |
0 | 141 | 1987 | 1971 |
901 |
|---|
| cabdaaddb |
0 | 142 | 739 | 2881 |
1238 |
|---|
| caddbbada |
0 | 142 | 1428 | 2072 |
1358 |
|---|
| cdabbaadd |
0 | 145 | 1994 | 1651 |
1210 |
|---|
| cadbbddaa |
0 | 145 | 1994 | 1651 |
1210 |
|---|
| cdbabadda |
0 | 149 | 2001 | 1727 |
1123 |
|---|
| cddaababd |
0 | 149 | 2377 | 972 |
1502 |
|---|
| caaddbdba |
0 | 149 | 2377 | 972 |
1502 |
|---|
| cdaadbadb |
0 | 154 | 1685 | 2342 |
819 |
|---|
| caaddbadb |
0 | 154 | 1878 | 2024 |
944 |
|---|
| cbaaddabd |
0 | 164 | 928 | 2840 |
1068 |
|---|
| cdbaaddab |
0 | 173 | 860 | 2576 |
1391 |
|---|
| cdbadbaad |
0 | 175 | 1887 | 1934 |
1004 |
|---|
| cadadbdba |
0 | 177 | 1897 | 1925 |
1001 |
|---|
| cdadababd |
0 | 177 | 1897 | 1925 |
1001 |
|---|
| cadaadbbd |
0 | 179 | 1165 | 1934 |
1722 |
|---|
| cbadbadda |
0 | 189 | 1930 | 2183 |
698 |
|---|
| cdbadadab |
0 | 190 | 1025 | 2888 |
897 |
|---|
| cabdadadb |
0 | 190 | 1025 | 2888 |
897 |
|---|
| cbdaaddba |
0 | 192 | 1110 | 2385 |
1313 |
|---|
| cbaddbada |
0 | 208 | 2045 | 2088 |
659 |
|---|
| cbddabaad |
0 | 210 | 2088 | 1533 |
1169 |
|---|
| cbaadbdda |
0 | 210 | 2088 | 1533 |
1169 |
|---|
| cddabaadb |
0 | 217 | 2301 | 1602 |
880 |
|---|
| caadbddab |
0 | 217 | 2301 | 1602 |
880 |
|---|
| cadaadbdb |
0 | 247 | 2459 | 1471 |
823 |
|---|
| cdbaadbda |
0 | 249 | 1377 | 2071 |
1303 |
|---|
| cabddabad |
0 | 249 | 1377 | 2071 |
1303 |
|---|
| cdabadabd |
0 | 261 | 2173 | 1577 |
989 |
|---|
| cabdadbda |
0 | 269 | 2266 | 1573 |
892 |
|---|
| cbabaddad |
0 | 271 | 2411 | 1609 |
709 |
|---|
| caddbadab |
0 | 272 | 1696 | 2112 |
920 |
|---|
| cbdbaadda |
0 | 274 | 1625 | 2238 |
863 |
|---|
| cdaaddbab |
0 | 280 | 1538 | 2374 |
808 |
|---|
| cadbbdada |
0 | 301 | 1793 | 1872 |
1034 |
|---|
| cdabbadad |
0 | 301 | 1793 | 1872 |
1034 |
|---|
| caddbbdaa |
0 | 311 | 1982 | 1840 |
867 |
|---|
| cddaadbba |
0 | 319 | 923 | 2118 |
1640 |
|---|
| caaddabbd |
0 | 319 | 923 | 2118 |
1640 |
|---|
| cdadbbada |
0 | 328 | 1116 | 1937 |
1619 |
|---|
| cbdadbaad |
0 | 339 | 1862 | 2035 |
764 |
|---|
| cbdaadbad |
0 | 371 | 1853 | 2206 |
570 |
|---|
| cbaddabda |
0 | 371 | 1853 | 2206 |
570 |
|---|
| cdbabdada |
0 | 423 | 1886 | 1990 |
701 |
|---|
| cabdbadad |
0 | 423 | 1886 | 1990 |
701 |
|---|
| cbadabdad |
0 | 473 | 2762 | 1445 |
320 |
|---|
| cbdadbada |
0 | 473 | 2762 | 1445 |
320 |
|---|
| cbabdaadd |
0 | 553 | 1947 | 1879 |
621 |
|---|
| cbdbaddaa |
0 | 553 | 1947 | 1879 |
621 |
|---|
| cadbabadd |
0 | 573 | 1994 | 1943 |
490 |
|---|
| caadbbadd |
0 | 584 | 1546 | 1647 |
1223 |
|---|
| cbabdadad |
0 | 603 | 2012 | 1783 |
602 |
|---|
| cbdbadada |
0 | 603 | 2012 | 1783 |
602 |
|---|
| cadbabdad |
0 | 614 | 2175 | 1785 |
426 |
|---|
| cdabdbada |
0 | 614 | 2175 | 1785 |
426 |
|---|
| caaddbabd |
0 | 616 | 1745 | 1982 |
657 |
|---|
| cddaabdba |
0 | 616 | 1745 | 1982 |
657 |
|---|
| caddbabda |
0 | 906 | 2491 | 1276 |
327 |
|---|
| cdbdbdaaa |
1 | 4 | 2190 | 900 |
1905 |
|---|
| cdddababa |
1 | 13 | 2426 | 856 |
1704 |
|---|
| cbdaaadbd |
1 | 20 | 2490 | 1588 |
901 |
|---|
| cbadddaba |
1 | 20 | 2490 | 1588 |
901 |
|---|
| cadaabdbd |
1 | 127 | 1168 | 2332 |
1372 |
|---|
| cdaddbaba |
1 | 127 | 1168 | 2332 |
1372 |
|---|
| cdbadadba |
1 | 137 | 1079 | 2174 |
1609 |
|---|
| caadbadbd |
1 | 159 | 1652 | 2077 |
1111 |
|---|
| cddabdaba |
1 | 159 | 1652 | 2077 |
1111 |
|---|
| cdabbadda |
1 | 181 | 1231 | 2314 |
1273 |
|---|
| cdaadbbda |
1 | 282 | 1253 | 2271 |
1193 |
|---|
| cadbbadda |
1 | 436 | 1695 | 1823 |
1045 |
|---|
| cdaadbbad |
1 | 473 | 1693 | 1698 |
1135 |
|---|
| cddabdbaa |
1 | 871 | 2293 | 1374 |
461 |
|---|
| caadbabdd |
1 | 871 | 2293 | 1374 |
461 |
|---|
| cdabdbaad |
1 | 887 | 2415 | 1327 |
370 |
|---|
| cdaaadbbd |
2 | 39 | 950 | 2126 |
1883 |
|---|
| cadddabba |
2 | 39 | 950 | 2126 |
1883 |
|---|
| cdbdbaaad |
2 | 46 | 1256 | 1335 |
2361 |
|---|
| cdaadbdba |
2 | 231 | 1894 | 1928 |
945 |
|---|
| cddabbaad |
2 | 330 | 2187 | 1575 |
906 |
|---|
| cdadbbdaa |
2 | 624 | 1793 | 1767 |
814 |
|---|
| cadabbadd |
2 | 624 | 1793 | 1767 |
814 |
|---|
| caddbadba |
3 | 154 | 1851 | 2003 |
989 |
|---|
| cadbadabd |
3 | 305 | 1706 | 1978 |
1008 |
|---|
| caadbdbad |
3 | 538 | 2064 | 1786 |
609 |
|---|
| cdababadd |
4 | 204 | 2731 | 1089 |
972 |
|---|
| cadbdbdaa |
4 | 204 | 2731 | 1089 |
972 |
|---|
| cadbadbad |
4 | 209 | 1915 | 2211 |
661 |
|---|
| cabdadbad |
4 | 298 | 1735 | 1980 |
983 |
|---|
| cdbadbada |
5 | 164 | 2270 | 1907 |
654 |
|---|
| caabddabd |
7 | 110 | 1290 | 1941 |
1652 |
|---|
| cddbaadba |
7 | 110 | 1290 | 1941 |
1652 |
|---|
| cabdaddba |
7 | 133 | 858 | 2050 |
1952 |
|---|
| cdbdabaad |
7 | 183 | 1844 | 1645 |
1321 |
|---|
| cabadbdda |
7 | 183 | 1844 | 1645 |
1321 |
|---|
| cdabadbad |
7 | 288 | 2170 | 1800 |
735 |
|---|
| cdababdad |
7 | 463 | 2321 | 1735 |
474 |
|---|
| cadbdbada |
7 | 463 | 2321 | 1735 |
474 |
|---|
| cdadbadba |
8 | 190 | 2022 | 2171 |
609 |
|---|
| cabaddabd |
8 | 230 | 1451 | 1930 |
1381 |
|---|
| cadabadbd |
9 | 182 | 1837 | 2235 |
737 |
|---|
| cdadbdaba |
9 | 182 | 1837 | 2235 |
737 |
|---|
| cadbdbaad |
9 | 252 | 1559 | 2034 |
1146 |
|---|
| cdababdda |
9 | 252 | 1559 | 2034 |
1146 |
|---|
| cadbadbda |
9 | 314 | 2062 | 1864 |
751 |
|---|
| cadddbaba |
10 | 32 | 1171 | 1301 |
2486 |
|---|
| cabdaadbd |
11 | 205 | 1618 | 1858 |
1308 |
|---|
| cdbaadabd |
12 | 106 | 888 | 2079 |
1915 |
|---|
| cadbaabdd |
18 | 135 | 1384 | 2292 |
1171 |
|---|
| cdabddbaa |
18 | 135 | 1384 | 2292 |
1171 |
|---|
| cdaadbabd |
20 | 655 | 1759 | 1875 |
691 |
|---|
| cabdbadda |
26 | 573 | 1850 | 1904 |
647 |
|---|
| cdabaadbd |
27 | 339 | 1464 | 1471 |
1699 |
|---|
| cdabadbda |
30 | 333 | 1852 | 2193 |
592 |
|---|
| cabaddbda |
31 | 354 | 1539 | 1451 |
1625 |
|---|
| cadbaadbd |
39 | 225 | 1221 | 2019 |
1496 |
|---|
| cadababdd |
46 | 603 | 1711 | 1843 |
797 |
|---|
| cdadbdbaa |
46 | 603 | 1711 | 1843 |
797 |
|---|
| cabaddbad |
47 | 207 | 1191 | 1940 |
1615 |
|---|
| cdbddaaba |
54 | 47 | 1048 | 507 |
3344 |
|---|
| cdbaaadbd |
62 | 74 | 1068 | 931 |
2865 |
|---|
| caddbdbaa |
66 | 315 | 1936 | 1275 |
1408 |
|---|
| cabadddba |
68 | 96 | 966 | 1030 |
2840 |
|---|
| cabadadbd |
73 | 124 | 1165 | 1392 |
2246 |
|---|
| cdbdadbaa |
74 | 302 | 1604 | 1888 |
1132 |
|---|
| cabadabdd |
74 | 302 | 1604 | 1888 |
1132 |
|---|
| cddbabaad |
75 | 338 | 1956 | 1116 |
1515 |
|---|
| cddbaabad |
88 | 218 | 1400 | 951 |
2343 |
|---|
| cadbddbaa |
110 | 206 | 1276 | 964 |
2444 |
|---|
| cdbddabaa |
120 | 81 | 1521 | 1089 |
2189 |
|---|
| cabaadbdd |
120 | 81 | 1521 | 1089 |
2189 |
|---|
| cddbadbaa |
151 | 546 | 1837 | 1733 |
733 |
|---|
| cddbdabaa |
205 | 88 | 1851 | 1396 |
1460 |
|---|
|
)3(X
)2X
(Y
)3 = 8 on Fl(2,3,4;6)
