10-1100-Assignment 1 Part 1 by cjeagle

Here I present a solution to MegaMinx. The puzzle is in the form of a regular dodecahedron, with each face capable of rotating. There are two versions to this puzzle. The first version, which I solve here, has a different colour on each face. The other version, which introduces parity issues, gives the same colour to opposite faces. I will only be considering the version with unique colours on each face. There are 132 tiles, which I have numbered from 0 to 131 to make coding easier. Here is a model, with numbering of the tiles (thanks to Amy Eagle for building this!):

Each face can be rotated clockwise or counterclockwise. Of course, we only need to consider one of these rotations, since the group generated will then contain the other as well. Here is a list of generating permutations which arises from rotating each face counterclockwise:

orange = [10 7 4 1 8 5 2 0 9 6 3 57 12 13 56 15 16 55 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 101 47 48 104 50 51 52 108 54 46 49 53 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 110 102 103 111 105 106 107 112 109 17 14 11 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 ]

grey = [0 1 2 112 4 5 115 7 8 9 119 17 14 11 18 15 12 21 19 16 13 20 55 23 24 58 26 27 61 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 10 56 57 6 59 60 3 62 63 64 65 22 67 68 25 70 71 28 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 72 113 114 69 116 117 118 66 120 121 122 123 124 125 126 127 128 129 130 131 ]

red = [0 1 2 3 4 5 6 7 8 9 10 11 12 66 14 15 67 17 18 19 68 21 28 25 22 29 26 23 32 30 27 24 31 61 34 35 62 37 38 65 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 20 16 63 64 13 77 78 79 69 70 71 72 73 74 75 76 39 36 33 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 ]

light blue = [0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 79 25 26 82 28 29 30 86 32 39 36 33 40 37 34 43 41 38 35 42 65 45 46 63 48 49 64 51 52 53 54 55 56 57 58 59 60 61 62 27 24 31 66 67 68 69 70 71 72 73 74 75 76 77 78 88 80 81 89 83 84 85 90 87 50 47 44 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 ]

light brown = [0 64 2 3 60 5 6 57 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 90 36 37 93 39 40 41 97 43 50 47 44 51 48 45 54 52 49 46 53 55 56 35 58 59 38 61 62 63 42 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 99 91 92 100 94 95 96 101 98 7 4 1 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 ]

purple = [0 11 12 13 4 5 6 7 8 9 10 22 23 24 14 15 16 17 18 19 20 21 33 34 35 25 26 27 28 29 30 31 32 44 45 46 36 37 38 39 40 41 42 43 1 2 3 47 48 49 50 51 52 53 54 61 58 55 62 59 56 65 63 60 57 64 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 ]

light green = [0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 118 119 120 22 23 24 25 26 27 21 19 30 31 20 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 72 69 66 73 70 67 76 74 71 68 75 28 78 79 29 81 82 32 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 124 127 121 77 122 123 80 125 126 83 128 129 130 131 ]

dark brown = [0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 71 68 75 33 34 35 36 37 38 32 30 41 42 31 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 121 69 70 122 72 73 74 123 76 83 80 77 84 81 78 87 85 82 79 86 39 89 90 40 92 93 43 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 94 91 88 124 125 126 127 128 129 130 131 ]

pink = [0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 85 86 87 44 45 46 47 48 49 43 41 52 53 42 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 126 123 130 94 91 88 95 92 89 98 96 93 90 97 50 100 101 51 103 104 54 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 105 124 125 102 127 128 129 99 131 ]

dark green = [53 1 2 3 4 5 6 54 52 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 96 97 98 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 129 130 131 105 102 99 106 103 100 109 107 104 101 108 7 111 112 8 114 115 0 117 118 119 120 121 122 123 124 125 126 127 128 113 116 110 ]

dark blue = [109 1 2 3 4 5 6 7 8 107 108 11 12 13 14 15 16 0 9 19 20 10 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 17 18 74 75 21 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 128 131 127 116 113 110 117 114 111 120 118 115 112 119 121 122 123 124 125 126 72 73 129 130 76 ]

magenta = [0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 117 120 116 77 78 79 80 81 82 76 74 85 86 75 88 89 90 91 92 93 83 84 96 97 87 99 100 101 102 103 104 94 95 107 108 98 110 111 112 113 114 115 105 106 118 119 109 127 124 121 128 125 122 131 129 126 123 130 ]

The group generated by these permutations has 100669616553523347122516032313645505168688116411019768627200000000000 elements, which is certainly higher than I can count. The complete C++ source code I used to find this number is at 10-1100-cjeagleA1Code (and includes the input of the generating permutations). The output file is here: 10-1100-cjeagleA1Output.