The statistics below are for puzzles with the left ring containing one color of balls and the right ring containing the other color (with one intersection of each color). Statistics on Hungarian Ring Puzzles of sizes 5 thru 16. Section 1 The number of moves to obtain all positions Section 2 The number of moves to obtain all positions A sequence of moves that gives the position with all colors interchanged. Section 3 The number of postions obtained after each number of moves. A sequence of moves that gives the position with all colors interchanged. Sequences of moves to obtain positions that appear to be of special interest. Section 1: Number of moves required Also lists how many positions require the maximal number of moves. When the rotation required to move one intersection point to the other is RELATIVELY PRIME TO THE RING SIZE, the number of moves required is r - 1 (where 'r' is the ring size). When the rotation required to move one intersection point to the other is ONE-THIRD OF THE RING SIZE, the number of moves required is r + r/3 - 2 (where 'r' is the ring size). In this case only, the position with all colors interchanged and its near twin with the intersection points not interchanged, are the only positions that require the full number of moves. 5:1 10 positions require 4 moves 6:1 2 positions require 6 moves 7:1 34 positions require 6 moves 7:2 34 positions require 6 moves 8:1 148 positions require 7 moves 8:2 64 positions require 7 moves 9:1 120 positions require 8 moves 9:2 2 positions require 10 moves 9:3 120 positions require 8 moves 10:1 6 positions require 10 moves 10:2 208 positions require 9 moves 10:3 6 positions require 10 moves 11:1 364 positions require 10 moves 11:2 364 positions require 10 moves 11:3 364 positions require 10 moves 11:4 364 positions require 10 moves 12:1 8 positions require 12 moves -- opposite reached in 11 moves 12:2 5,444 positions require 11 moves 12:3 2 positions require 14 moves 12:4 708 positions require 11 moves 13:1 1,216 positions require 12 moves 13:2 1,216 positions require 12 moves 13:3 1,216 positions require 12 moves 13:4 1,216 positions require 12 moves 13:5 1,216 positions require 12 moves 14:1 20 positions require 14 moves 14:2 2,356 positions require 13 moves 14:3 20 positions require 14 moves 14:4 2,356 positions require 13 moves 14:5 20 positions require 14 moves 15:1 4,060 positions require 14 moves 15:2 6 positions require 16 moves 15:3 4,060 positions require 14 moves 15:4 2 positions require 18 moves 15:5 6 positions require 16 moves 15:6 4,060 positions require 14 moves 16:1 29,482 positions require 15 moves 16:2 8,196 positions require 15 moves 16:3 219,540 positions require 15 moves 16:4 8,196 positions require 15 moves 16:5 29,482 positions require 15 moves 16:6 8,196 positions require 15 moves Section 2: Moves that obtain the 'opposite' position In all cases except 12:1 (ring size 12 with 1 ball between the intersections) the maximal number of moves is required to interchange all of the colors. 5:1 10 positions require 4 moves Opposite: [oo(o)o(-)][--(o)-(-)] LaRaLaRa 6:1 2 positions require 6 moves Opposite: [ooo(o)o(-)][---(o)-(-)] LaRaLbRdLeRc 7:1 34 positions require 6 moves Opposite: [oooo(o)o(-)][----(o)-(-)] LbRaLaRcLcRf 7:2 34 positions require 6 moves Opposite: [ooo(o)oo(-)][---(o)--(-)] LaRaLaRaLaRa 8:1 148 positions require 7 moves Opposite: [ooooo(o)o(-)][-----(o)-(-)] LaRaLaRcLcRaLa 8:2 64 positions require 7 moves Opposite: [oooo(o)oo(-)][----(o)--(-)] LaRbLaRbLaRbLd 9:1 120 positions require 8 moves Opposite: [oooooo(o)o(-)][------(o)-(-)] LaRaLaRcLcRaLaRa 9:2 2 positions require 10 moves Opposite: [ooooo(o)oo(-)][-----(o)--(-)] LaRaLaRbLaRbLaRfLdRb 9:3 120 positions require 8 moves Opposite: [oooo(o)ooo(-)][----(o)---(-)] LaRaLaRaLaRaLaRa 10:1 6 positions require 10 moves Opposite: [ooooooo(o)o(-)][-------(o)-(-)] LaRaLaRcLcRaLdRbLgRi 10:2 208 positions require 9 moves Opposite: [oooooo(o)oo(-)][------(o)--(-)] LaRbLbRbLbRbLdRbLh 10:3 6 positions require 10 moves Opposite: [ooooo(o)ooo(-)][-----(o)---(-)] LaRaLaRaLaRaLbRfLiRe 11:1 364 positions require 10 moves Opposite: [oooooooo(o)o(-)][--------(o)-(-)] LbRaLaRcLcRaLaRcLcRj 11:2 364 positions require 10 moves Opposite: [ooooooo(o)oo(-)][-------(o)--(-)] LcRaLaRaLaRdLdRaLaRi 11:3 364 positions require 10 moves Opposite: [oooooo(o)ooo(-)][------(o)---(-)] LaRaLbRbLaRcLbRcLcRf 11:4 364 positions require 10 moves Opposite: [ooooo(o)oooo(-)][-----(o)----(-)] LaRaLaRaLaRaLaRaLaRa 12:1 8 positions require 12 moves -- opposite reached in 11 moves Opposite: [ooooooooo(o)o(-)][---------(o)-(-)] LaRaLaRcLcRaLaRcLcRaLa 12:2 5,444 positions require 11 moves Opposite: [oooooooo(o)oo(-)][--------(o)--(-)] LaRaLaRaLaRdLdRaLaRaLa 12:3 2 positions require 14 moves Opposite: [ooooooo(o)ooo(-)][-------(o)---(-)] LaRaLaRaLcRaLaRgLaRfLhRgLaRf 12:4 708 positions require 11 moves Opposite: [oooooo(o)oooo(-)][------(o)----(-)] LaRbLaRbLaRbLaRbLaRbLf 13:1 1,216 positions require 12 moves Opposite: [oooooooooo(o)o(-)][----------(o)-(-)] LaRaLaRcLcRaLaRcLcRaLaRa 13:2 1,216 positions require 12 moves Opposite: [ooooooooo(o)oo(-)][---------(o)--(-)] LaRaLaRaLaRdLdRaLaRaLaRa 13:3 1,216 positions require 12 moves Opposite: [oooooooo(o)ooo(-)][--------(o)---(-)] LbRaLbRbLaRcLbRbLcRcLbRg 13:4 1,216 positions require 12 moves Opposite: [ooooooo(o)oooo(-)][-------(o)----(-)] LbRaLaRbLbRaLaRcLcRcLcRi 13:5 1,216 positions require 12 moves Opposite: [oooooo(o)ooooo(-)][------(o)-----(-)] LaRaLaRaLaRaLaRaLaRaLaRa 14:1 20 positions require 14 moves Opposite: [ooooooooooo(o)o(-)][-----------(o)-(-)] LaRaLaRcLcRaLaRcLcRaLdRbLkRm 14:2 2,356 positions require 13 moves Opposite: [oooooooooo(o)oo(-)][----------(o)--(-)] LaRbLaRbLaRbLdRbLaRbLaRbLd 14:3 20 positions require 14 moves Opposite: [ooooooooo(o)ooo(-)][---------(o)---(-)] LaRaLbRaLaRaLgRdLaRaLhRaLcRk 14:4 2,356 positions require 13 moves Opposite: [oooooooo(o)oooo(-)][--------(o)----(-)] LaRbLaRbLbRbLaRbLcRbLdRbLm 14:5 20 positions require 14 moves Opposite: [ooooooo(o)ooooo(-)][-------(o)-----(-)] LaRaLaRaLaRaLaRaLaRaLbRhLmRg 15:1 4,060 positions require 14 moves Opposite: [oooooooooooo(o)o(-)][------------(o)-(-)] LbRaLaRcLcRaLaRcLcRaLaRcLcRn 15:2 6 positions require 16 moves Opposite: [ooooooooooo(o)oo(-)][-----------(o)--(-)] LaRaLaRaLaRdLdRaLaReLaRkLdRcLmRn 15:3 4,060 positions require 14 moves Opposite: [oooooooooo(o)ooo(-)][----------(o)---(-)] LdRaLaRaLaRaLaReLeRaLaRaLaRl 15:4 2 positions require 18 moves Opposite: [ooooooooo(o)oooo(-)][---------(o)----(-)] LaRaLaRaLaRcLaRaLaRbLaRaLaRiLfRaLaRc 15:5 6 positions require 16 moves Opposite: [oooooooo(o)ooooo(-)][--------(o)-----(-)] LaRaLaRaLaRaLaRaLaRbLaRhLgRfLaRb 15:6 4,060 positions require 14 moves Opposite: [ooooooo(o)oooooo(-)][-------(o)------(-)] LaRaLaRaLaRaLaRaLaRaLaRaLaRa 16:1 29,482 positions require 15 moves Opposite: [ooooooooooooo(o)o(-)][-------------(o)-(-)] LaRaLaRcLcRaLaRcLcRaLaRcLcRaLa 16:2 8,196 positions require 15 moves Opposite: [oooooooooooo(o)oo(-)][------------(o)--(-)] LaRbLbRbLbRbLbRbLbRbLbRbLdRbLn 16:3 219,540 positions require 15 moves Opposite: [ooooooooooo(o)ooo(-)][-----------(o)---(-)] LaRaLaRaLaRaLaReLeRaLaRaLaRaLa 16:4 8,196 positions require 15 moves Opposite: [oooooooooo(o)oooo(-)][----------(o)----(-)] LaRbLbRbLbRbLbRbLbRbLdRbLbRbLl 16:5 29,482 positions require 15 moves Opposite: [ooooooooo(o)ooooo(-)][---------(o)-----(-)] LaRaLaRcLbRaLaRcLaRaLcRcLdRaLa 16:6 8,196 positions require 15 moves Opposite: [oooooooo(o)oooooo(-)][--------(o)------(-)] LaRbLaRbLaRbLaRbLaRbLaRbLaRbLh Section 3: 'All the news thats fit to print.' Statistics on each puzzle are preceeded by the size of the puzzle and the number of balls between the intersections. 9:2 signifies a puzzles with rings with 9 balls, each of which have 2 balls within the other ring. For each puzzle, a shortest path solution is given, i.e. a sequence of moves of minimial length that interchanges the color of all of the balls. Opposite 12,869> [ooooo(o)oo(-)][-----(o)--(-)] LaRaLaRbLaRbLaRfLdRb The line above shows the 12,869th position found by manipulating the 9:2 puzzle. This is the 'opposite' position, the one with the colors of all of the balls interchanged. 'LaRaLaRbLaRbLaRfLdRb' is the list of moves that first reached this position. 'L' signifies a rotation of the left ring, 'R' a rotation of the right ring. 'a' is a move 1 place to the right, 'b' two places etc. 'To the right' refers to the textual representation of the rings as shown above. The graphical representation of the left ring would rotate counter-clockwise and the right ring clockwise. In the textual representation the right-most item in each ring is the upper intersection of the rings -- the other item in parentheses being the lower intersection. 5:1 70 positions possible. Rings with 5 items and 1 item between. After 1 move 8 positions are reached. After 2 moves 30 positions are reached. After 3 moves 60 positions are reached. After 4 moves 70 positions are reached. <- done Opposite 61> [oo(o)o(-)][--(o)-(-)] LaRaLaRa Opposite 63> [oo(-)o(o)][--(-)-(o)] LaRaLaRc 6:1 252 positions possible. Rings with 6 items and 1 item between. After 1 move 10 positions are reached. After 2 moves 48 positions are reached. After 3 moves 132 positions are reached. After 4 moves 222 positions are reached. After 5 moves 250 positions are reached. After 6 moves 252 positions are reached. <- done Opposite 251> [ooo(o)o(-)][---(o)-(-)] LaRaLbRdLeRc Opposite 252> [ooo(-)o(o)][---(-)-(o)] LaRaLbRdLeRe 7:1 924 positions possible. Rings with 7 items and 1 item between. After 1 move 12 positions are reached. After 2 moves 70 positions are reached. After 3 moves 260 positions are reached. After 4 moves 624 positions are reached. After 5 moves 890 positions are reached. After 6 moves 924 positions are reached. <- done Opposite 921> [oooo(-)o(o)][----(-)-(o)] LbRaLaRcLcRa Opposite 924> [oooo(o)o(-)][----(o)-(-)] LbRaLaRcLcRf 7:2 924 positions possible. Rings with 7 items and 2 items between. After 1 move 12 positions are reached. After 2 moves 70 positions are reached. After 3 moves 260 positions are reached. After 4 moves 624 positions are reached. After 5 moves 890 positions are reached. After 6 moves 924 positions are reached. <- done Opposite 891> [ooo(o)oo(-)][---(o)--(-)] LaRaLaRaLaRa Opposite 894> [ooo(-)oo(o)][---(-)--(o)] LaRaLaRaLaRd 8:1 3,432 positions possible. Rings with 8 items and 1 item between. After 1 move 14 positions are reached. After 2 moves 96 positions are reached. After 3 moves 444 positions are reached. After 4 moves 1,364 positions are reached. After 5 moves 2,554 positions are reached. After 6 moves 3,284 positions are reached. After 7 moves 3,432 positions are reached. <- done Opposite 3,324> [ooooo(o)o(-)][-----(o)-(-)] LaRaLaRcLcRaLa Opposite 3,325> [ooooo(-)o(o)][-----(-)-(o)] LaRaLaRcLcRaLg 8:2 3,432 positions possible. Rings with 8 items and 2 items between. After 1 move 14 positions are reached. After 2 moves 96 positions are reached. After 3 moves 444 positions are reached. After 4 moves 1,346 positions are reached. After 5 moves 2,618 positions are reached. After 6 moves 3,368 positions are reached. After 7 moves 3,432 positions are reached. <- done Opposite 3,421> [oooo(-)oo(o)][----(-)--(o)] LaRbLaRbLaRbLa Opposite 3,422> [oooo(o)oo(-)][----(o)--(-)] LaRbLaRbLaRbLd 9:1 12,870 positions possible. Rings with 9 items and 1 item between. After 1 move 16 positions are reached. After 2 moves 126 positions are reached. After 3 moves 700 positions are reached. After 4 moves 2,548 positions are reached. After 5 moves 6,330 positions are reached. After 6 moves 10,772 positions are reached. After 7 moves 12,750 positions are reached. After 8 moves 12,870 positions are reached. <- done Opposite 12,803> [oooooo(o)o(-)][------(o)-(-)] LaRaLaRcLcRaLaRa Opposite 12,805> [oooooo(-)o(o)][------(-)-(o)] LaRaLaRcLcRaLaRc 9:2 12,870 positions possible. Rings with 9 items and 2 items between. After 1 move 16 positions are reached. After 2 moves 126 positions are reached. After 3 moves 684 positions are reached. After 4 moves 2,196 positions are reached. After 5 moves 4,780 positions are reached. After 6 moves 9,360 positions are reached. After 7 moves 12,114 positions are reached. After 8 moves 12,690 positions are reached. After 9 moves 12,868 positions are reached. After 10 moves 12,870 positions are reached. <- done Opposite 12,869> [ooooo(o)oo(-)][-----(o)--(-)] LaRaLaRbLaRbLaRfLdRb Opposite 12,870> [ooooo(-)oo(o)][-----(-)--(o)] LaRaLaRbLaRbLaRfLdRe PEDIGREE for position <12869> Left ring Right ring Moves 1> [-----(-)--(o)][ooooo(-)oo(o)] none 2> [o----(-)--(-)][ooooo(-)oo(-)] La 17> [o----(o)--(o)][-oooo(o)-o(o)] LaRa 127> [oo---(-)o-(-)][-oooo(-)-o(-)] LaRaLa 686> [oo---(o)o-(-)][o--oo(o)o-(-)] LaRaLaRb 2,204> [-oo--(-)oo(-)][o--oo(-)o-(-)] LaRaLaRbLa 4,816> [-oo--(o)oo(o)][--o--(o)o-(o)] LaRaLaRbLaRb 9,421> [o-oo-(-)oo(o)][--o--(-)o-(o)] LaRaLaRbLaRbLa 12,169> [o-oo-(o)oo(o)][---o-(o)--(o)] LaRaLaRbLaRbLaRf 12,757> [ooooo(-)oo(-)][---o-(-)--(-)] LaRaLaRbLaRbLaRfLd 12,869> [ooooo(o)oo(-)][-----(o)--(-)] LaRaLaRbLaRbLaRfLdRb 9:3 12,870 positions possible. Rings with 9 items and 3 items between. After 1 move 16 positions are reached. After 2 moves 126 positions are reached. After 3 moves 700 positions are reached. After 4 moves 2,548 positions are reached. After 5 moves 6,330 positions are reached. After 6 moves 10,772 positions are reached. After 7 moves 12,750 positions are reached. After 8 moves 12,870 positions are reached. <- done Opposite 12,751> [oooo(o)ooo(-)][----(o)---(-)] LaRaLaRaLaRaLaRa Opposite 12,755> [oooo(-)ooo(o)][----(-)---(o)] LaRaLaRaLaRaLaRe 10:1 48,620 positions possible. Rings with 10 items and 1 item between. After 1 move 18 positions are reached. After 2 moves 160 positions are reached. After 3 moves 1,040 positions are reached. After 4 moves 4,410 positions are reached. After 5 moves 13,790 positions are reached. After 6 moves 28,790 positions are reached. After 7 moves 43,898 positions are reached. After 8 moves 48,450 positions are reached. After 9 moves 48,614 positions are reached. After 10 moves 48,620 positions are reached. <- done Opposite 48,618> [ooooooo(-)o(o)][-------(-)-(o)] LaRaLaRcLcRaLdRbLgRa Opposite 48,620> [ooooooo(o)o(-)][-------(o)-(-)] LaRaLaRcLcRaLdRbLgRi 10:2 48,620 positions possible. Rings with 10 items and 2 items between. After 1 move 18 positions are reached. After 2 moves 160 positions are reached. After 3 moves 1,040 positions are reached. After 4 moves 4,398 positions are reached. After 5 moves 13,308 positions are reached. After 6 moves 29,056 positions are reached. After 7 moves 43,480 positions are reached. After 8 moves 48,412 positions are reached. After 9 moves 48,620 positions are reached. <- done Opposite 48,617> [oooooo(-)oo(o)][------(-)--(o)] LaRbLbRbLbRbLdRbLe Opposite 48,618> [oooooo(o)oo(-)][------(o)--(-)] LaRbLbRbLbRbLdRbLh 10:3 48,620 positions possible. Rings with 10 items and 3 items between. After 1 move 18 positions are reached. After 2 moves 160 positions are reached. After 3 moves 1,040 positions are reached. After 4 moves 4,410 positions are reached. After 5 moves 13,790 positions are reached. After 6 moves 28,790 positions are reached. After 7 moves 43,898 positions are reached. After 8 moves 48,450 positions are reached. After 9 moves 48,614 positions are reached. After 10 moves 48,620 positions are reached. <- done Opposite 48,615> [ooooo(o)ooo(-)][-----(o)---(-)] LaRaLaRaLaRaLbRfLiRe Opposite 48,617> [ooooo(-)ooo(o)][-----(-)---(o)] LaRaLaRaLaRaLbRfLiRi 11:1 184,756 positions possible. Rings with 11 items and 1 item between. After 1 move 20 positions are reached. After 2 moves 198 positions are reached. After 3 moves 1,476 positions are reached. After 4 moves 7,088 positions are reached. After 5 moves 25,266 positions are reached. After 6 moves 67,770 positions are reached. After 7 moves 127,680 positions are reached. After 8 moves 172,354 positions are reached. After 9 moves 184,392 positions are reached. After 10 moves 184,756 positions are reached. <- done Opposite 184,751> [oooooooo(-)o(o)][--------(-)-(o)] LbRaLaRcLcRaLaRcLcRa Opposite 184,756> [oooooooo(o)o(-)][--------(o)-(-)] LbRaLaRcLcRaLaRcLcRj 11:2 184,756 positions possible. Rings with 11 items and 2 items between. After 1 move 20 positions are reached. After 2 moves 198 positions are reached. After 3 moves 1,476 positions are reached. After 4 moves 7,088 positions are reached. After 5 moves 25,266 positions are reached. After 6 moves 67,770 positions are reached. After 7 moves 127,680 positions are reached. After 8 moves 172,354 positions are reached. After 9 moves 184,392 positions are reached. After 10 moves 184,756 positions are reached. <- done Opposite 184,751> [ooooooo(-)oo(o)][-------(-)--(o)] LcRaLaRaLaRdLdRaLaRa Opposite 184,756> [ooooooo(o)oo(-)][-------(o)--(-)] LcRaLaRaLaRdLdRaLaRi 11:3 184,756 positions possible. Rings with 11 items and 3 items between. After 1 move 20 positions are reached. After 2 moves 198 positions are reached. After 3 moves 1,476 positions are reached. After 4 moves 7,088 positions are reached. After 5 moves 25,266 positions are reached. After 6 moves 67,770 positions are reached. After 7 moves 127,680 positions are reached. After 8 moves 172,354 positions are reached. After 9 moves 184,392 positions are reached. After 10 moves 184,756 positions are reached. <- done Opposite 184,728> [oooooo(o)ooo(-)][------(o)---(-)] LaRaLbRbLaRcLbRcLcRf Opposite 184,731> [oooooo(-)ooo(o)][------(-)---(o)] LaRaLbRbLaRcLbRcLcRj 11:4 184,756 positions possible. Rings with 11 items and 4 items between. After 1 move 20 positions are reached. After 2 moves 198 positions are reached. After 3 moves 1,476 positions are reached. After 4 moves 7,088 positions are reached. After 5 moves 25,266 positions are reached. After 6 moves 67,770 positions are reached. After 7 moves 127,680 positions are reached. After 8 moves 172,354 positions are reached. After 9 moves 184,392 positions are reached. After 10 moves 184,756 positions are reached. <- done Opposite 184,393> [ooooo(o)oooo(-)][-----(o)----(-)] LaRaLaRaLaRaLaRaLaRa Opposite 184,398> [ooooo(-)oooo(o)][-----(-)----(o)] LaRaLaRaLaRaLaRaLaRf 12:1 705,432 positions possible. Rings with 12 items and 1 item between. After 1 move 22 positions are reached. After 2 moves 240 positions are reached. After 3 moves 2,020 positions are reached. After 4 moves 10,834 positions are reached. After 5 moves 44,586 positions are reached. After 6 moves 140,484 positions are reached. After 7 moves 317,770 positions are reached. After 8 moves 536,884 positions are reached. After 9 moves 661,446 positions are reached. After 10 moves 702,930 positions are reached. After 11 moves 705,424 positions are reached. After 12 moves 705,432 positions are reached. <- done Opposite 704,403> [ooooooooo(o)o(-)][---------(o)-(-)] LaRaLaRcLcRaLaRcLcRaLa Opposite 704,404> [ooooooooo(-)o(o)][---------(-)-(o)] LaRaLaRcLcRaLaRcLcRaLk PEDIGREE for position <704403> Left ring Right ring Moves 1> [---------(-)-(o)][ooooooooo(-)o(o)] none 2> [o--------(-)-(-)][ooooooooo(-)o(-)] La 23> [o--------(o)-(o)][-oooooooo(o)-(o)] LaRa 241> [oo-------(-)o(-)][-oooooooo(-)-(-)] LaRaLa 2,023> [oo-------(o)o(o)][----ooooo(o)o(o)] LaRaLaRc 10,857> [ooooo----(-)-(-)][----ooooo(-)o(-)] LaRaLaRcLc 44,730> [ooooo----(o)-(o)][-----oooo(o)-(o)] LaRaLaRcLcRa 141,455> [oooooo---(-)o(-)][-----oooo(-)-(-)] LaRaLaRcLcRaLa 321,413> [oooooo---(o)o(o)][--------o(o)o(o)] LaRaLaRcLcRaLaRc 545,525> [ooooooooo(-)-(-)][--------o(-)o(-)] LaRaLaRcLcRaLaRcLc 670,134> [ooooooooo(o)-(o)][---------(o)-(o)] LaRaLaRcLcRaLaRcLcRa 704,403> [ooooooooo(o)o(-)][---------(o)-(-)] LaRaLaRcLcRaLaRcLcRaLa 705,425> [-oo--oo--(o)o(-)][oo--oo--o(o)-(-)] LaRaLbRaLbReLkRkLbRcLaRb 705,426> [-oo--oo--(o)o(-)][-oo--oo--(o)o(-)] LaRaLbRaLbReLkRkLbRcLaRc 705,427> [oo--oo--o(o)-(-)][oo--oo--o(o)-(-)] LaRaLbRaLbReLkRkLcRcLkRb 705,428> [oo--oo--o(o)-(-)][-oo--oo--(o)o(-)] LaRaLbRaLbReLkRkLcRcLkRc 705,429> [--oo--oo-(-)o(o)][--oo--oo-(-)o(o)] LaRaLeReLeRdLeRaLeRhLjRa 705,430> [--oo--oo-(-)o(o)][o--oo--oo(-)-(o)] LaRaLeReLeRdLeRaLeRhLjRb 705,431> [o--oo--oo(-)-(o)][--oo--oo-(-)o(o)] LaRaLeReLeRdLjRiLjRdLiRa 705,432> [o--oo--oo(-)-(o)][o--oo--oo(-)-(o)] LaRaLeReLeRdLjRiLjRdLiRb 12:2 705,432 positions possible. Rings with 12 items and 2 items between. After 1 move 22 positions are reached. After 2 moves 240 positions are reached. After 3 moves 2,020 positions are reached. After 4 moves 10,708 positions are reached. After 5 moves 42,460 positions are reached. After 6 moves 136,612 positions are reached. After 7 moves 316,180 positions are reached. After 8 moves 523,636 positions are reached. After 9 moves 646,794 positions are reached. After 10 moves 699,988 positions are reached. After 11 moves 705,432 positions are reached. <- done Opposite 701,104> [oooooooo(o)oo(-)][--------(o)--(-)] LaRaLaRaLaRdLdRaLaRaLa Opposite 701,105> [oooooooo(-)oo(o)][--------(-)--(o)] LaRaLaRaLaRdLdRaLaRaLj 12:3 705,432 positions possible. Rings with 12 items and 3 items between. After 1 move 22 positions are reached. After 2 moves 240 positions are reached. After 3 moves 1,986 positions are reached. After 4 moves 9,438 positions are reached. After 5 moves 32,964 positions are reached. After 6 moves 101,508 positions are reached. After 7 moves 212,370 positions are reached. After 8 moves 407,904 positions are reached. After 9 moves 565,404 positions are reached. After 10 moves 668,292 positions are reached. After 11 moves 700,494 positions are reached. After 12 moves 703,950 positions are reached. After 13 moves 705,430 positions are reached. After 14 moves 705,432 positions are reached. <- done Opposite 705,431> [ooooooo(o)ooo(-)][-------(o)---(-)] LaRaLaRaLcRaLaRgLaRfLhRgLaRf Opposite 705,432> [ooooooo(-)ooo(o)][-------(-)---(o)] LaRaLaRaLcRaLaRgLaRfLhRgLaRj PEDIGREE for position <705431> Left ring Right ring Moves 1> [-------(-)---(o)][ooooooo(-)ooo(o)] none 2> [o------(-)---(-)][ooooooo(-)ooo(-)] La 23> [o------(o)---(o)][-oooooo(o)-oo(o)] LaRa 241> [oo-----(-)o--(-)][-oooooo(-)-oo(-)] LaRaLa 1,987> [oo-----(o)o--(o)][--ooooo(o)--o(o)] LaRaLaRa 9,441> [--ooo--(-)--o(o)][--ooooo(-)--o(o)] LaRaLaRaLc 32,983> [--ooo--(o)--o(o)][o--oooo(o)---(o)] LaRaLaRaLcRa 101,605> [o--ooo-(-)o--(o)][o--oooo(-)---(o)] LaRaLaRaLcRaLa 212,991> [o--ooo-(o)o--(o)][oo----o(o)--o(o)] LaRaLaRaLcRaLaRg 409,325> [oo--ooo(-)oo-(-)][oo----o(-)--o(-)] LaRaLaRaLcRaLaRgLa 568,842> [oo--ooo(o)oo-(-)][o---o-o(o)---(-)] LaRaLaRaLcRaLaRgLaRf 671,145> [oooooo-(-)oo-(-)][o---o-o(-)---(-)] LaRaLaRaLcRaLaRgLaRfLh 701,504> [oooooo-(o)oo-(o)][-o-----(o)---(o)] LaRaLaRaLcRaLaRgLaRfLhRg 704,779> [ooooooo(-)ooo(-)][-o-----(-)---(-)] LaRaLaRaLcRaLaRgLaRfLhRgLa 705,431> [ooooooo(o)ooo(-)][-------(o)---(-)] LaRaLaRaLcRaLaRgLaRfLhRgLaRf 12:4 705,432 positions possible. Rings with 12 items and 4 items between. After 1 move 22 positions are reached. After 2 moves 240 positions are reached. After 3 moves 2,020 positions are reached. After 4 moves 10,834 positions are reached. After 5 moves 44,410 positions are reached. After 6 moves 141,224 positions are reached. After 7 moves 324,656 positions are reached. After 8 moves 545,370 positions are reached. After 9 moves 676,098 positions are reached. After 10 moves 704,724 positions are reached. After 11 moves 705,432 positions are reached. <- done Opposite 705,419> [oooooo(-)oooo(o)][------(-)----(o)] LaRbLaRbLaRbLaRbLaRbLa Opposite 705,420> [oooooo(o)oooo(-)][------(o)----(-)] LaRbLaRbLaRbLaRbLaRbLf 13:1 2,704,156 positions possible. Rings with 13 items and 1 item between. After 1 move 24 positions are reached. After 2 moves 286 positions are reached. After 3 moves 2,684 positions are reached. After 4 moves 15,876 positions are reached. After 5 moves 73,498 positions are reached. After 6 moves 269,708 positions are reached. After 7 moves 733,940 positions are reached. After 8 moves 1,510,598 positions are reached. After 9 moves 2,260,728 positions are reached. After 10 moves 2,634,658 positions are reached. After 11 moves 2,702,940 positions are reached. After 12 moves 2,704,156 positions are reached. <- done Opposite 2,703,916> [oooooooooo(o)o(-)][----------(o)-(-)] LaRaLaRcLcRaLaRcLcRaLaRa Opposite 2,703,918> [oooooooooo(-)o(o)][----------(-)-(o)] LaRaLaRcLcRaLaRcLcRaLaRc 13:2 2,704,156 positions possible. Rings with 13 items and 2 items between. After 1 move 24 positions are reached. After 2 moves 286 positions are reached. After 3 moves 2,684 positions are reached. After 4 moves 15,876 positions are reached. After 5 moves 73,498 positions are reached. After 6 moves 269,708 positions are reached. After 7 moves 733,940 positions are reached. After 8 moves 1,510,598 positions are reached. After 9 moves 2,260,728 positions are reached. After 10 moves 2,634,658 positions are reached. After 11 moves 2,702,940 positions are reached. After 12 moves 2,704,156 positions are reached. <- done Opposite 2,703,382> [ooooooooo(o)oo(-)][---------(o)--(-)] LaRaLaRaLaRdLdRaLaRaLaRa Opposite 2,703,385> [ooooooooo(-)oo(o)][---------(-)--(o)] LaRaLaRaLaRdLdRaLaRaLaRd 13:3 2,704,156 positions possible. Rings with 13 items and 3 items between. After 1 move 24 positions are reached. After 2 moves 286 positions are reached. After 3 moves 2,684 positions are reached. After 4 moves 15,876 positions are reached. After 5 moves 73,498 positions are reached. After 6 moves 269,708 positions are reached. After 7 moves 733,940 positions are reached. After 8 moves 1,510,598 positions are reached. After 9 moves 2,260,728 positions are reached. After 10 moves 2,634,658 positions are reached. After 11 moves 2,702,940 positions are reached. After 12 moves 2,704,156 positions are reached. <- done Opposite 2,704,153> [oooooooo(o)ooo(-)][--------(o)---(-)] LbRaLbRbLaRcLbRbLcRcLbRg Opposite 2,704,155> [oooooooo(-)ooo(o)][--------(-)---(o)] LbRaLbRbLaRcLbRbLcRcLbRk 13:4 2,704,156 positions possible. Rings with 13 items and 4 items between. After 1 move 24 positions are reached. After 2 moves 286 positions are reached. After 3 moves 2,684 positions are reached. After 4 moves 15,876 positions are reached. After 5 moves 73,498 positions are reached. After 6 moves 269,708 positions are reached. After 7 moves 733,940 positions are reached. After 8 moves 1,510,598 positions are reached. After 9 moves 2,260,728 positions are reached. After 10 moves 2,634,658 positions are reached. After 11 moves 2,702,940 positions are reached. After 12 moves 2,704,156 positions are reached. <- done Opposite 2,704,131> [ooooooo(-)oooo(o)][-------(-)----(o)] LbRaLaRbLbRaLaRcLcRcLcRa Opposite 2,704,135> [ooooooo(o)oooo(-)][-------(o)----(-)] LbRaLaRbLbRaLaRcLcRcLcRi 13:5 2,704,156 positions possible. Rings with 13 items and 5 items between. After 1 move 24 positions are reached. After 2 moves 286 positions are reached. After 3 moves 2,684 positions are reached. After 4 moves 15,876 positions are reached. After 5 moves 73,498 positions are reached. After 6 moves 269,708 positions are reached. After 7 moves 733,940 positions are reached. After 8 moves 1,510,598 positions are reached. After 9 moves 2,260,728 positions are reached. After 10 moves 2,634,658 positions are reached. After 11 moves 2,702,940 positions are reached. After 12 moves 2,704,156 positions are reached. <- done Opposite 2,702,941> [oooooo(o)ooooo(-)][------(o)-----(-)] LaRaLaRaLaRaLaRaLaRaLaRa Opposite 2,702,947> [oooooo(-)ooooo(o)][------(-)-----(o)] LaRaLaRaLaRaLaRaLaRaLaRg 14:1 10,400,600 positions possible. Rings with 14 items and 1 item between. After 1 move 26 positions are reached. After 2 moves 336 positions are reached. After 3 moves 3,480 positions are reached. After 4 moves 22,478 positions are reached. After 5 moves 115,900 positions are reached. After 6 moves 480,662 positions are reached. After 7 moves 1,505,868 positions are reached. After 8 moves 3,691,814 positions are reached. After 9 moves 6,696,086 positions are reached. After 10 moves 9,222,836 positions are reached. After 11 moves 10,304,986 positions are reached. After 12 moves 10,399,238 positions are reached. After 13 moves 10,400,580 positions are reached. After 14 moves 10,400,600 positions are reached. <- done Opposite 10,400,597> [ooooooooooo(-)o(o)][-----------(-)-(o)] LaRaLaRcLcRaLaRcLcRaLdRbLkRa Opposite 10,400,600> [ooooooooooo(o)o(-)][-----------(o)-(-)] LaRaLaRcLcRaLaRcLcRaLdRbLkRm 14:2 10,400,600 positions possible. Rings with 14 items and 2 items between. After 1 move 26 positions are reached. After 2 moves 336 positions are reached. After 3 moves 3,480 positions are reached. After 4 moves 22,478 positions are reached. After 5 moves 115,900 positions are reached. After 6 moves 480,832 positions are reached. After 7 moves 1,511,180 positions are reached. After 8 moves 3,713,332 positions are reached. After 9 moves 6,708,308 positions are reached. After 10 moves 9,203,366 positions are reached. After 11 moves 10,232,886 positions are reached. After 12 moves 10,398,244 positions are reached. After 13 moves 10,400,600 positions are reached. <- done Opposite 10,400,593> [oooooooooo(-)oo(o)][----------(-)--(o)] LaRbLaRbLaRbLdRbLaRbLaRbLa Opposite 10,400,594> [oooooooooo(o)oo(-)][----------(o)--(-)] LaRbLaRbLaRbLdRbLaRbLaRbLd 14:3 10,400,600 positions possible. Rings with 14 items and 3 items between. After 1 move 26 positions are reached. After 2 moves 336 positions are reached. After 3 moves 3,480 positions are reached. After 4 moves 22,478 positions are reached. After 5 moves 115,900 positions are reached. After 6 moves 480,662 positions are reached. After 7 moves 1,505,868 positions are reached. After 8 moves 3,691,814 positions are reached. After 9 moves 6,696,086 positions are reached. After 10 moves 9,222,836 positions are reached. After 11 moves 10,304,986 positions are reached. After 12 moves 10,399,238 positions are reached. After 13 moves 10,400,580 positions are reached. After 14 moves 10,400,600 positions are reached. <- done Opposite 10,400,597> [ooooooooo(-)ooo(o)][---------(-)---(o)] LaRaLbRaLaRaLgRdLaRaLhRaLcRa Opposite 10,400,600> [ooooooooo(o)ooo(-)][---------(o)---(-)] LaRaLbRaLaRaLgRdLaRaLhRaLcRk 14:4 10,400,600 positions possible. Rings with 14 items and 4 items between. After 1 move 26 positions are reached. After 2 moves 336 positions are reached. After 3 moves 3,480 positions are reached. After 4 moves 22,478 positions are reached. After 5 moves 115,900 positions are reached. After 6 moves 480,832 positions are reached. After 7 moves 1,511,180 positions are reached. After 8 moves 3,713,332 positions are reached. After 9 moves 6,708,308 positions are reached. After 10 moves 9,203,366 positions are reached. After 11 moves 10,232,886 positions are reached. After 12 moves 10,398,244 positions are reached. After 13 moves 10,400,600 positions are reached. <- done Opposite 10,400,597> [oooooooo(-)oooo(o)][--------(-)----(o)] LaRbLaRbLbRbLaRbLcRbLdRbLh Opposite 10,400,598> [oooooooo(o)oooo(-)][--------(o)----(-)] LaRbLaRbLbRbLaRbLcRbLdRbLm 14:5 10,400,600 positions possible. Rings with 14 items and 5 items between. After 1 move 26 positions are reached. After 2 moves 336 positions are reached. After 3 moves 3,480 positions are reached. After 4 moves 22,478 positions are reached. After 5 moves 115,900 positions are reached. After 6 moves 480,662 positions are reached. After 7 moves 1,505,868 positions are reached. After 8 moves 3,691,814 positions are reached. After 9 moves 6,696,086 positions are reached. After 10 moves 9,222,836 positions are reached. After 11 moves 10,304,986 positions are reached. After 12 moves 10,399,238 positions are reached. After 13 moves 10,400,580 positions are reached. After 14 moves 10,400,600 positions are reached. <- done Opposite 10,400,581> [ooooooo(o)ooooo(-)][-------(o)-----(-)] LaRaLaRaLaRaLaRaLaRaLbRhLmRg Opposite 10,400,584> [ooooooo(-)ooooo(o)][-------(-)-----(o)] LaRaLaRaLaRaLaRaLaRaLbRhLmRm 15:1 40,116,600 positions possible. Rings with 15 items and 1 item between. After 1 move 28 positions are reached. After 2 moves 390 positions are reached. After 3 moves 4,420 positions are reached. After 4 moves 30,928 positions are reached. After 5 moves 175,658 positions are reached. After 6 moves 810,986 positions are reached. After 7 moves 2,887,360 positions are reached. After 8 moves 8,265,988 positions are reached. After 9 moves 17,722,054 positions are reached. After 10 moves 29,027,010 positions are reached. After 11 moves 36,854,676 positions are reached. After 12 moves 39,727,850 positions are reached. After 13 moves 40,112,540 positions are reached. After 14 moves 40,116,600 positions are reached. <- done Opposite 40,116,593> [oooooooooooo(-)o(o)][------------(-)-(o)] LbRaLaRcLcRaLaRcLcRaLaRcLcRa Opposite 40,116,600> [oooooooooooo(o)o(-)][------------(o)-(-)] LbRaLaRcLcRaLaRcLcRaLaRcLcRn 15:2 40,116,600 positions possible. Rings with 15 items and 2 items between. After 1 move 28 positions are reached. After 2 moves 390 positions are reached. After 3 moves 4,420 positions are reached. After 4 moves 30,950 positions are reached. After 5 moves 177,420 positions are reached. After 6 moves 816,740 positions are reached. After 7 moves 2,994,542 positions are reached. After 8 moves 8,541,580 positions are reached. After 9 moves 18,687,516 positions are reached. After 10 moves 29,588,210 positions are reached. After 11 moves 37,733,660 positions are reached. After 12 moves 39,849,340 positions are reached. After 13 moves 40,105,518 positions are reached. After 14 moves 40,116,350 positions are reached. After 15 moves 40,116,594 positions are reached. After 16 moves 40,116,600 positions are reached. <- done Opposite 40,116,598> [ooooooooooo(-)oo(o)][-----------(-)--(o)] LaRaLaRaLaRdLdRaLaReLaRkLdRcLmRb Opposite 40,116,600> [ooooooooooo(o)oo(-)][-----------(o)--(-)] LaRaLaRaLaRdLdRaLaReLaRkLdRcLmRn 40,116,595> [ooooo-ooooo(o)oo(o)][-----------(o)--(o)] LaRaLaRaLaRaLdRdLaRfLcRjLbRaLkRb 40,116,596> [ooooo-ooooo(-)oo(o)][-----o-----(-)--(o)] LaRaLaRaLaRaLdRdLaRfLcRjLnRaLnRe 40,116,597> [ooooo-ooooo(o)oo(-)][-----o-----(o)--(-)] LaRaLaRaLaRaLdRdLaRfLcRjLnRaLnRk 40,116,598> [ooooooooooo(-)oo(o)][-----------(-)--(o)] LaRaLaRaLaRdLdRaLaReLaRkLdRcLmRb 40,116,599> [ooooooooooo(-)oo(-)][-----o-----(-)--(-)] LaRaLaRaLaRdLdRaLaReLaRkLdRcLmRh 40,116,600> [ooooooooooo(o)oo(-)][-----------(o)--(-)] LaRaLaRaLaRdLdRaLaReLaRkLdRcLmRn 15:3 40,116,600 positions possible. Rings with 15 items and 3 items between. After 1 move 28 positions are reached. After 2 moves 390 positions are reached. After 3 moves 4,420 positions are reached. After 4 moves 30,928 positions are reached. After 5 moves 175,658 positions are reached. After 6 moves 810,986 positions are reached. After 7 moves 2,887,360 positions are reached. After 8 moves 8,265,988 positions are reached. After 9 moves 17,722,054 positions are reached. After 10 moves 29,027,010 positions are reached. After 11 moves 36,854,676 positions are reached. After 12 moves 39,727,850 positions are reached. After 13 moves 40,112,540 positions are reached. After 14 moves 40,116,600 positions are reached. <- done Opposite 40,116,593> [oooooooooo(-)ooo(o)][----------(-)---(o)] LdRaLaRaLaRaLaReLeRaLaRaLaRa Opposite 40,116,600> [oooooooooo(o)ooo(-)][----------(o)---(-)] LdRaLaRaLaRaLaReLeRaLaRaLaRl 15:4 40,116,600 positions possible. Rings with 15 items and 4 items between. After 1 move 28 positions are reached. After 2 moves 390 positions are reached. After 3 moves 4,362 positions are reached. After 4 moves 27,402 positions are reached. After 5 moves 133,978 positions are reached. After 6 moves 559,962 positions are reached. After 7 moves 1,677,402 positions are reached. After 8 moves 4,827,330 positions are reached. After 9 moves 9,867,510 positions are reached. After 10 moves 18,575,568 positions are reached. After 11 moves 26,782,128 positions are reached. After 12 moves 34,666,776 positions are reached. After 13 moves 38,223,340 positions are reached. After 14 moves 39,673,200 positions are reached. After 15 moves 40,076,268 positions are reached. After 16 moves 40,103,448 positions are reached. After 17 moves 40,116,598 positions are reached. After 18 moves 40,116,600 positions are reached. <- done Opposite 40,116,599> [ooooooooo(o)oooo(-)][---------(o)----(-)] LaRaLaRaLaRcLaRaLaRbLaRaLaRiLfRaLaRc Opposite 40,116,600> [ooooooooo(-)oooo(o)][---------(-)----(o)] LaRaLaRaLaRcLaRaLaRbLaRaLaRiLfRaLaRh PEDIGREE for position <40116599> Left ring Right ring Moves 1> [---------(-)----(o)][ooooooooo(-)oooo(o)] none 2> [o--------(-)----(-)][ooooooooo(-)oooo(-)] La 29> [o--------(o)----(o)][-oooooooo(o)-ooo(o)] LaRa 391> [oo-------(-)o---(-)][-oooooooo(-)-ooo(-)] LaRaLa 4,363> [oo-------(o)o---(o)][--ooooooo(o)--oo(o)] LaRaLaRa 27,403> [ooo------(-)oo--(-)][--ooooooo(-)--oo(-)] LaRaLaRaLa 133,981> [ooo------(o)oo--(-)][oo---oooo(o)oo--(-)] LaRaLaRaLaRc 559,987> [-ooo-----(-)ooo-(-)][oo---oooo(-)oo--(-)] LaRaLaRaLaRcLa 1,677,647> [-ooo-----(o)ooo-(-)][-oo---ooo(o)-oo-(-)] LaRaLaRaLaRcLaRa 4,828,930> [--ooo----(-)oooo(-)][-oo---ooo(-)-oo-(-)] LaRaLaRaLaRcLaRaLa 9,877,039> [--ooo----(o)oooo(o)][---oo---o(o)o--o(o)] LaRaLaRaLaRcLaRaLaRb 18,610,987> [o--ooo---(-)oooo(o)][---oo---o(-)o--o(o)] LaRaLaRaLaRcLaRaLaRbLa 26,902,753> [o--ooo---(o)oooo(o)][o---oo---(o)-o--(o)] LaRaLaRaLaRcLaRaLaRbLaRa 34,852,850> [oo--ooo--(-)oooo(o)][o---oo---(-)-o--(o)] LaRaLaRaLaRcLaRaLaRbLaRaLa 38,466,838> [oo--ooo--(o)oooo(o)][-----o--o(o)---o(o)] LaRaLaRaLaRcLaRaLaRbLaRaLaRi 39,824,136> [oooooooo-(-)ooo-(-)][-----o--o(-)---o(-)] LaRaLaRaLaRcLaRaLaRbLaRaLaRiLf 40,094,964> [oooooooo-(o)ooo-(o)][------o--(o)----(o)] LaRaLaRaLaRcLaRaLaRbLaRaLaRiLfRa 40,115,949> [ooooooooo(-)oooo(-)][------o--(-)----(-)] LaRaLaRaLaRcLaRaLaRbLaRaLaRiLfRaLa 40,116,599> [ooooooooo(o)oooo(-)][---------(o)----(-)] LaRaLaRaLaRcLaRaLaRbLaRaLaRiLfRaLaRc 15:5 40,116,600 positions possible. Rings with 15 items and 5 items between. After 1 move 28 positions are reached. After 2 moves 390 positions are reached. After 3 moves 4,420 positions are reached. After 4 moves 30,950 positions are reached. After 5 moves 177,420 positions are reached. After 6 moves 816,740 positions are reached. After 7 moves 2,994,542 positions are reached. After 8 moves 8,541,580 positions are reached. After 9 moves 18,687,516 positions are reached. After 10 moves 29,588,210 positions are reached. After 11 moves 37,733,660 positions are reached. After 12 moves 39,849,340 positions are reached. After 13 moves 40,105,518 positions are reached. After 14 moves 40,116,350 positions are reached. After 15 moves 40,116,594 positions are reached. After 16 moves 40,116,600 positions are reached. <- done Opposite 40,116,595> [oooooooo(o)ooooo(-)][--------(o)-----(-)] LaRaLaRaLaRaLaRaLaRbLaRhLgRfLaRb Opposite 40,116,597> [oooooooo(-)ooooo(o)][--------(-)-----(o)] LaRaLaRaLaRaLaRaLaRbLaRhLgRfLaRh 40,116,595> [oooooooo(o)ooooo(-)][--------(o)-----(-)] LaRaLaRaLaRaLaRaLaRbLaRhLgRfLaRb 40,116,596> [oooooooo(-)ooooo(-)][--------(-)--o--(-)] LaRaLaRaLaRaLaRaLaRbLaRhLgRfLaRe 40,116,597> [oooooooo(-)ooooo(o)][--------(-)-----(o)] LaRaLaRaLaRaLaRaLaRbLaRhLgRfLaRh 40,116,598> [oooooooo(o)oo-oo(o)][--------(o)-----(o)] LaRaLaRaLaRaLaRaLcRaLaRaLmRgLnRa 40,116,599> [oooooooo(o)oo-oo(-)][--------(o)--o--(-)] LaRaLaRaLaRaLaRaLcRaLdRgLjRaLhRj 40,116,600> [oooooooo(-)oo-oo(o)][--------(-)--o--(o)] LaRaLaRaLaRaLaRaLcRaLdRgLjRaLhRm PEDIGREE for position <40116595> Left ring Right ring Moves 1> [--------(-)-----(o)][oooooooo(-)ooooo(o)] none 2> [o-------(-)-----(-)][oooooooo(-)ooooo(-)] La 29> [o-------(o)-----(o)][-ooooooo(o)-oooo(o)] LaRa 391> [oo------(-)o----(-)][-ooooooo(-)-oooo(-)] LaRaLa 4,421> [oo------(o)o----(o)][--oooooo(o)--ooo(o)] LaRaLaRa 30,951> [ooo-----(-)oo---(-)][--oooooo(-)--ooo(-)] LaRaLaRaLa 177,421> [ooo-----(o)oo---(o)][---ooooo(o)---oo(o)] LaRaLaRaLaRa 816,741> [oooo----(-)ooo--(-)][---ooooo(-)---oo(-)] LaRaLaRaLaRaLa 2,994,543> [oooo----(o)ooo--(o)][----oooo(o)----o(o)] LaRaLaRaLaRaLaRa 8,541,581> [ooooo---(-)oooo-(-)][----oooo(-)----o(-)] LaRaLaRaLaRaLaRaLa 18,687,518> [ooooo---(o)oooo-(-)][o-----oo(o)o----(-)] LaRaLaRaLaRaLaRaLaRb 29,588,220> [-ooooo--(-)ooooo(-)][o-----oo(-)o----(-)] LaRaLaRaLaRaLaRaLaRbLa 37,733,705> [-ooooo--(o)ooooo(o)][o-o-----(o)-----(o)] LaRaLaRaLaRaLaRaLaRbLaRh 39,849,352> [ooooooo-(o)oooo-(-)][o-o-----(o)-----(-)] LaRaLaRaLaRaLaRaLaRbLaRhLg 40,105,536> [ooooooo-(o)oooo-(o)][------o-(o)-----(o)] LaRaLaRaLaRaLaRaLaRbLaRhLgRf 40,116,351> [oooooooo(-)ooooo(-)][------o-(-)-----(-)] LaRaLaRaLaRaLaRaLaRbLaRhLgRfLa 40,116,595> [oooooooo(o)ooooo(-)][--------(o)-----(-)] LaRaLaRaLaRaLaRaLaRbLaRhLgRfLaRb 15:6 40,116,600 positions possible. Rings with 15 items and 6 items between. After 1 move 28 positions are reached. After 2 moves 390 positions are reached. After 3 moves 4,420 positions are reached. After 4 moves 30,928 positions are reached. After 5 moves 175,658 positions are reached. After 6 moves 810,986 positions are reached. After 7 moves 2,887,360 positions are reached. After 8 moves 8,265,988 positions are reached. After 9 moves 17,722,054 positions are reached. After 10 moves 29,027,010 positions are reached. After 11 moves 36,854,676 positions are reached. After 12 moves 39,727,850 positions are reached. After 13 moves 40,112,540 positions are reached. After 14 moves 40,116,600 positions are reached. <- done Opposite 40,112,541> [ooooooo(o)oooooo(-)][-------(o)------(-)] LaRaLaRaLaRaLaRaLaRaLaRaLaRa Opposite 40,112,548> [ooooooo(-)oooooo(o)][-------(-)------(o)] LaRaLaRaLaRaLaRaLaRaLaRaLaRh 16:1 155,117,520 positions possible. Rings with 16 items and 1 item between. After 1 move 30 positions are reached. After 2 moves 448 positions are reached. After 3 moves 5,516 positions are reached. After 4 moves 41,538 positions are reached. After 5 moves 257,546 positions are reached. After 6 moves 1,306,920 positions are reached. After 7 moves 5,191,464 positions are reached. After 8 moves 16,929,400 positions are reached. After 9 moves 42,207,350 positions are reached. After 10 moves 82,262,408 positions are reached. After 11 moves 121,890,900 positions are reached. After 12 moves 146,560,268 positions are reached. After 13 moves 153,608,174 positions are reached. After 14 moves 155,088,038 positions are reached. After 15 moves 155,117,520 positions are reached. <- done Opposite 155,116,639> [ooooooooooooo(o)o(-)][-------------(o)-(-)] LaRaLaRcLcRaLaRcLcRaLaRcLcRaLa Opposite 155,116,640> [ooooooooooooo(-)o(o)][-------------(-)-(o)] LaRaLaRcLcRaLaRcLcRaLaRcLcRaLo PEDIGREE for position <155,116,639> Left ring Right ring Moves 1> [-------------(-)-(o)][ooooooooooooo(-)o(o)] none 2> [o------------(-)-(-)][ooooooooooooo(-)o(-)] La 31> [o------------(o)-(o)][-oooooooooooo(o)-(o)] LaRa 449> [oo-----------(-)o(-)][-oooooooooooo(-)-(-)] LaRaLa 5,519> [oo-----------(o)o(o)][----ooooooooo(o)o(o)] LaRaLaRc 41,569> [ooooo--------(-)-(-)][----ooooooooo(-)o(-)] LaRaLaRcLc 257,858> [ooooo--------(o)-(o)][-----oooooooo(o)-(o)] LaRaLaRcLcRa 1,310,565> [oooooo-------(-)o(-)][-----oooooooo(-)-(-)] LaRaLaRcLcRaLa 5,219,247> [oooooo-------(o)o(o)][--------ooooo(o)o(o)] LaRaLaRcLcRaLaRc 17,110,939> [ooooooooo----(-)-(-)][--------ooooo(-)o(-)] LaRaLaRcLcRaLaRcLc 42,864,697> [ooooooooo----(o)-(o)][---------oooo(o)-(o)] LaRaLaRcLcRaLaRcLcRa 84,064,122> [oooooooooo---(-)o(-)][---------oooo(-)-(-)] LaRaLaRcLcRaLaRcLcRaLa 124,442,950> [oooooooooo---(o)o(o)][------------o(o)o(o)] LaRaLaRcLcRaLaRcLcRaLaRc 148,439,689> [ooooooooooooo(-)-(-)][------------o(-)o(-)] LaRaLaRcLcRaLaRcLcRaLaRcLc 154,284,950> [ooooooooooooo(o)-(o)][-------------(o)-(o)] LaRaLaRcLcRaLaRcLcRaLaRcLcRa 155,116,639> [ooooooooooooo(o)o(-)][-------------(o)-(-)] LaRaLaRcLcRaLaRcLcRaLaRcLcRaLa 16:2 155,117,520 positions possible. Rings with 16 items and 2 items between. After 1 move 30 positions are reached. After 2 moves 448 positions are reached. After 3 moves 5,516 positions are reached. After 4 moves 41,538 positions are reached. After 5 moves 257,546 positions are reached. After 6 moves 1,306,920 positions are reached. After 7 moves 5,191,620 positions are reached. After 8 moves 16,966,202 positions are reached. After 9 moves 42,309,084 positions are reached. After 10 moves 82,101,252 positions are reached. After 11 moves 121,869,842 positions are reached. After 12 moves 146,646,894 positions are reached. After 13 moves 154,158,956 positions are reached. After 14 moves 155,109,324 positions are reached. After 15 moves 155,117,520 positions are reached. <- done Opposite 155,117,507> [oooooooooooo(-)oo(o)][------------(-)--(o)] LaRbLbRbLbRbLbRbLbRbLbRbLdRbLk Opposite 155,117,508> [oooooooooooo(o)oo(-)][------------(o)--(-)] LaRbLbRbLbRbLbRbLbRbLbRbLdRbLn PEDIGREE for position <155,117,508> Left ring Right ring Moves 1> [------------(-)--(o)][oooooooooooo(-)oo(o)] none 2> [o-----------(-)--(-)][oooooooooooo(-)oo(-)] La 32> [o-----------(o)--(o)][o-oooooooooo(o)o-(o)] LaRb 465> [-oo---------(-)-o(-)][o-oooooooooo(-)o-(-)] LaRbLb 5,716> [-oo---------(o)-o(o)][--o-oooooooo(o)o-(o)] LaRbLbRb 44,180> [oo-oo-------(-)-o(-)][--o-oooooooo(-)o-(-)] LaRbLbRbLb 285,194> [oo-oo-------(o)-o(o)][----o-oooooo(o)o-(o)] LaRbLbRbLbRb 1,534,450> [oooo-oo-----(-)-o(-)][----o-oooooo(-)o-(-)] LaRbLbRbLbRbLb 6,395,657> [oooo-oo-----(o)-o(o)][------o-oooo(o)o-(o)] LaRbLbRbLbRbLbRb 21,746,973> [oooooo-oo---(-)-o(-)][------o-oooo(-)o-(-)] LaRbLbRbLbRbLbRbLb 52,942,653> [oooooo-oo---(o)-o(o)][--------o-oo(o)o-(o)] LaRbLbRbLbRbLbRbLbRb 98,682,772> [oooooooo-oo-(-)-o(-)][--------o-oo(-)o-(-)] LaRbLbRbLbRbLbRbLbRbLb 133,763,366> [oooooooo-oo-(o)-o(o)][----------o-(o)o-(o)] LaRbLbRbLbRbLbRbLbRbLbRb 151,409,597> [o-oooooooooo(-)oo(-)][----------o-(-)o-(-)] LaRbLbRbLbRbLbRbLbRbLbRbLd 154,755,401> [o-oooooooooo(o)oo(o)][------------(o)--(o)] LaRbLbRbLbRbLbRbLbRbLbRbLdRb 155,117,508> [oooooooooooo(o)oo(-)][------------(o)--(-)] LaRbLbRbLbRbLbRbLbRbLbRbLdRbLn 16:3 155,117,520 positions possible. Rings with 16 items and 3 items between. After 1 move 30 positions are reached. After 2 moves 448 positions are reached. After 3 moves 5,516 positions are reached. After 4 moves 40,916 positions are reached. After 5 moves 246,826 positions are reached. After 6 moves 1,250,116 positions are reached. After 7 moves 4,832,968 positions are reached. After 8 moves 15,675,032 positions are reached. After 9 moves 38,796,726 positions are reached. After 10 moves 77,350,232 positions are reached. After 11 moves 113,810,356 positions are reached. After 12 moves 141,156,300 positions are reached. After 13 moves 150,759,106 positions are reached. After 14 moves 154,897,980 positions are reached. After 15 moves 155,117,520 positions are reached. <- done Opposite 154,930,712> [ooooooooooo(o)ooo(-)][-----------(o)---(-)] LaRaLaRaLaRaLaReLeRaLaRaLaRaLa Opposite 154,930,713> [ooooooooooo(-)ooo(o)][-----------(-)---(o)] LaRaLaRaLaRaLaReLeRaLaRaLaRaLm PEDIGREE for position <154,930,713> Left ring Right ring Moves 1> [-----------(-)---(o)][ooooooooooo(-)ooo(o)] none 2> [o----------(-)---(-)][ooooooooooo(-)ooo(-)] La 31> [o----------(o)---(o)][-oooooooooo(o)-oo(o)] LaRa 449> [oo---------(-)o--(-)][-oooooooooo(-)-oo(-)] LaRaLa 5,517> [oo---------(o)o--(o)][--ooooooooo(o)--o(o)] LaRaLaRa 40,917> [ooo--------(-)oo-(-)][--ooooooooo(-)--o(-)] LaRaLaRaLa 246,827> [ooo--------(o)oo-(o)][---oooooooo(o)---(o)] LaRaLaRaLaRa 1,250,117> [oooo-------(-)ooo(-)][---oooooooo(-)---(-)] LaRaLaRaLaRaLa 4,832,973> [oooo-------(o)ooo(o)][--------ooo(o)ooo(o)] LaRaLaRaLaRaLaRe 15,675,093> [ooooooooo--(-)---(-)][--------ooo(-)ooo(-)] LaRaLaRaLaRaLaReLe 38,797,081> [ooooooooo--(o)---(o)][---------oo(o)-oo(o)] LaRaLaRaLaRaLaReLeRa 77,352,710> [oooooooooo-(-)o--(-)][---------oo(-)-oo(-)] LaRaLaRaLaRaLaReLeRaLa 113,820,147> [oooooooooo-(o)o--(o)][----------o(o)--o(o)] LaRaLaRaLaRaLaReLeRaLaRa 141,189,758> [ooooooooooo(-)oo-(-)][----------o(-)--o(-)] LaRaLaRaLaRaLaReLeRaLaRaLa 150,828,588> [ooooooooooo(o)oo-(o)][-----------(o)---(o)] LaRaLaRaLaRaLaReLeRaLaRaLaRa 154,930,713> [ooooooooooo(-)ooo(o)][-----------(-)---(o)] LaRaLaRaLaRaLaReLeRaLaRaLaRaLm 16:4 155,117,520 positions possible. Rings with 16 items and 4 items between. After 1 move 30 positions are reached. After 2 moves 448 positions are reached. After 3 moves 5,516 positions are reached. After 4 moves 41,538 positions are reached. After 5 moves 257,546 positions are reached. After 6 moves 1,306,920 positions are reached. After 7 moves 5,191,620 positions are reached. After 8 moves 16,966,202 positions are reached. After 9 moves 42,309,084 positions are reached. After 10 moves 82,101,252 positions are reached. After 11 moves 121,869,842 positions are reached. After 12 moves 146,646,894 positions are reached. After 13 moves 154,158,956 positions are reached. After 14 moves 155,109,324 positions are reached. After 15 moves 155,117,520 positions are reached. <- done Opposite 155,117,506> [oooooooooo(-)oooo(o)][----------(-)----(o)] LaRbLbRbLbRbLbRbLbRbLdRbLbRbLg Opposite 155,117,507> [oooooooooo(o)oooo(-)][----------(o)----(-)] LaRbLbRbLbRbLbRbLbRbLdRbLbRbLl PEDIGREE for position <155,117,507> Left ring Right ring Moves 1> [----------(-)----(o)][oooooooooo(-)oooo(o)] none 2> [o---------(-)----(-)][oooooooooo(-)oooo(-)] La 32> [o---------(o)----(o)][o-oooooooo(o)o-oo(o)] LaRb 465> [-oo-------(-)-o--(-)][o-oooooooo(-)o-oo(-)] LaRbLb 5,715> [-oo-------(o)-o--(o)][o-o-oooooo(o)o-o-(o)] LaRbLbRb 44,039> [-o-oo-----(-)-o-o(-)][o-o-oooooo(-)o-o-(-)] LaRbLbRbLb 282,266> [-o-oo-----(o)-o-o(o)][--o-o-oooo(o)o-o-(o)] LaRbLbRbLbRb 1,505,476> [oo-o-oo---(-)-o-o(-)][--o-o-oooo(-)o-o-(-)] LaRbLbRbLbRbLb 6,222,447> [oo-o-oo---(o)-o-o(o)][----o-o-oo(o)o-o-(o)] LaRbLbRbLbRbLbRb 21,060,687> [oooo-o-oo-(-)-o-o(-)][----o-o-oo(-)o-o-(-)] LaRbLbRbLbRbLbRbLb 51,734,129> [oooo-o-oo-(o)-o-o(o)][------o-o-(o)o-o-(o)] LaRbLbRbLbRbLbRbLbRb 97,472,676> [o-oooooo-o(-)oo-o(-)][------o-o-(-)o-o-(-)] LaRbLbRbLbRbLbRbLbRbLd 133,629,768> [o-oooooo-o(o)oo-o(o)][--------o-(o)--o-(o)] LaRbLbRbLbRbLbRbLbRbLdRb 151,435,530> [ooo-oooooo(-)oooo(-)][--------o-(-)--o-(-)] LaRbLbRbLbRbLbRbLbRbLdRbLb 154,760,566> [ooo-oooooo(o)oooo(o)][----------(o)----(o)] LaRbLbRbLbRbLbRbLbRbLdRbLbRb 155,117,507> [oooooooooo(o)oooo(-)][----------(o)----(-)] LaRbLbRbLbRbLbRbLbRbLdRbLbRbLl 16:5 155,117,520 positions possible. Rings with 16 items and 5 items between. After 1 move 30 positions are reached. After 2 moves 448 positions are reached. After 3 moves 5,516 positions are reached. After 4 moves 41,538 positions are reached. After 5 moves 257,546 positions are reached. After 6 moves 1,306,920 positions are reached. After 7 moves 5,191,464 positions are reached. After 8 moves 16,929,400 positions are reached. After 9 moves 42,207,350 positions are reached. After 10 moves 82,262,408 positions are reached. After 11 moves 121,890,900 positions are reached. After 12 moves 146,560,268 positions are reached. After 13 moves 153,608,174 positions are reached. After 14 moves 155,088,038 positions are reached. After 15 moves 155,117,520 positions are reached. <- done Opposite 155,117,366> [ooooooooo(o)ooooo(-)][---------(o)-----(-)] LaRaLaRcLbRaLaRcLaRaLcRcLdRaLa Opposite 155,117,367> [ooooooooo(-)ooooo(o)][---------(-)-----(o)] LaRaLaRcLbRaLaRcLaRaLcRcLdRaLk PEDIGREE for position <155,117,366> Left ring Right ring Moves 1> [---------(-)-----(o)][ooooooooo(-)ooooo(o)] none 2> [o--------(-)-----(-)][ooooooooo(-)ooooo(-)] La 31> [o--------(o)-----(o)][-oooooooo(o)-oooo(o)] LaRa 449> [oo-------(-)o----(-)][-oooooooo(-)-oooo(-)] LaRaLa 5,519> [oo-------(o)o----(o)][oo--ooooo(o)oo--o(o)] LaRaLaRc 41,568> [-ooo-----(-)-oo--(-)][oo--ooooo(-)oo--o(-)] LaRaLaRcLb 257,888> [-ooo-----(o)-oo--(o)][-oo--oooo(o)-oo--(o)] LaRaLaRcLbRa 1,310,813> [o-ooo----(-)o-oo-(-)][-oo--oooo(-)-oo--(-)] LaRaLaRcLbRaLa 5,224,953> [o-ooo----(o)o-oo-(o)][----oo--o(o)oo--o(o)] LaRaLaRcLbRaLaRc 17,161,326> [oo-ooo---(-)oo-oo(-)][----oo--o(-)oo--o(-)] LaRaLaRcLbRaLaRcLa 43,182,742> [oo-ooo---(o)oo-oo(o)][-----oo--(o)-oo--(o)] LaRaLaRcLbRaLaRcLaRa 85,151,607> [ooooo-ooo(-)--ooo(-)][-----oo--(-)-oo--(-)] LaRaLaRcLbRaLaRcLaRaLc 125,945,992> [ooooo-ooo(o)--ooo(o)][--------o(o)----o(o)] LaRaLaRcLbRaLaRcLaRaLcRc 149,370,908> [ooooooooo(-)oooo-(-)][--------o(-)----o(-)] LaRaLaRcLbRaLaRcLaRaLcRcLd 154,366,524> [ooooooooo(o)oooo-(o)][---------(o)-----(o)] LaRaLaRcLbRaLaRcLaRaLcRcLdRa 155,117,366> [ooooooooo(o)ooooo(-)][---------(o)-----(-)] LaRaLaRcLbRaLaRcLaRaLcRcLdRaLa 16:6 155,117,520 positions possible. Rings with 16 items and 6 items between. After 1 move 30 positions are reached. After 2 moves 448 positions are reached. After 3 moves 5,516 positions are reached. After 4 moves 41,538 positions are reached. After 5 moves 257,546 positions are reached. After 6 moves 1,306,920 positions are reached. After 7 moves 5,191,620 positions are reached. After 8 moves 16,966,202 positions are reached. After 9 moves 42,309,084 positions are reached. After 10 moves 82,101,252 positions are reached. After 11 moves 121,869,842 positions are reached. After 12 moves 146,646,894 positions are reached. After 13 moves 154,158,956 positions are reached. After 14 moves 155,109,324 positions are reached. After 15 moves 155,117,520 positions are reached. <- done Opposite 155,117,505> [oooooooo(-)oooooo(o)][--------(-)------(o)] LaRbLaRbLaRbLaRbLaRbLaRbLaRbLa Opposite 155,117,506> [oooooooo(o)oooooo(-)][--------(o)------(-)] LaRbLaRbLaRbLaRbLaRbLaRbLaRbLh PEDIGREE for position <155,117,506> Left ring Right ring Moves 1> [--------(-)------(o)][oooooooo(-)oooooo(o)] none 2> [o-------(-)------(-)][oooooooo(-)oooooo(-)] La 32> [o-------(o)------(o)][o-oooooo(o)o-oooo(o)] LaRb 464> [oo------(-)o-----(-)][o-oooooo(-)o-oooo(-)] LaRbLa 5,702> [oo------(o)o-----(o)][o-o-oooo(o)o-o-oo(o)] LaRbLaRb 43,976> [ooo-----(-)oo----(-)][o-o-oooo(-)o-o-oo(-)] LaRbLaRbLa 283,147> [ooo-----(o)oo----(o)][o-o-o-oo(o)o-o-o-(o)] LaRbLaRbLaRb 1,512,616> [oooo----(-)ooo---(-)][o-o-o-oo(-)o-o-o-(-)] LaRbLaRbLaRbLa 6,281,334> [oooo----(o)ooo---(o)][--o-o-o-(o)o-o-o-(o)] LaRbLaRbLaRbLaRb 21,220,650> [ooooo---(-)oooo--(-)][--o-o-o-(-)o-o-o-(-)] LaRbLaRbLaRbLaRbLa 52,169,126> [ooooo---(o)oooo--(o)][----o-o-(o)--o-o-(o)] LaRbLaRbLaRbLaRbLaRb 97,440,549> [oooooo--(-)ooooo-(-)][----o-o-(-)--o-o-(-)] LaRbLaRbLaRbLaRbLaRbLa 133,639,128> [oooooo--(o)ooooo-(o)][------o-(o)----o-(o)] LaRbLaRbLaRbLaRbLaRbLaRb 151,337,256> [ooooooo-(-)oooooo(-)][------o-(-)----o-(-)] LaRbLaRbLaRbLaRbLaRbLaRbLa 154,752,245> [ooooooo-(o)oooooo(o)][--------(o)------(o)] LaRbLaRbLaRbLaRbLaRbLaRbLaRb 155,117,506> [oooooooo(o)oooooo(-)][--------(o)------(-)] LaRbLaRbLaRbLaRbLaRbLaRbLaRbLh