super_perm.txt about super permutations 3! number of permutations of 1, 2, 3 = 6 possible (1 2 3) (1 3 2) (2 1 3) (2 3 1) (3 1 2) (3 2 1) a "super permutation" is one string that has every permutation in the string 1 2 3 1 2 1 3 2 1 9 entries 1 2 3 2 3 1 3 1 2 2 1 3 1 3 2 3 2 1 optimum 4! number of permutations of 1, 2, 3, 4 = 24 possible (1 2 3 4 ) (1 2 4 3 ) (1 3 2 4 ) (1 3 4 2 ) (1 4 2 3 ) (1 4 3 2 ) (2 1 3 4 ) (2 1 4 3 ) (2 3 1 4 ) (2 3 4 1 ) (2 4 1 3 ) (2 4 3 1 ) (3 1 2 4 ) (3 1 4 2 ) (3 2 1 4 ) (3 2 4 1 ) (3 4 1 2 ) (3 4 2 1 ) (4 1 2 3 ) (4 1 3 2 ) (4 2 1 3 ) (4 2 3 1 ) (4 3 1 2 ) (4 3 2 1 ) optimum super permutation 33 entries 1 2 3 4 1 2 3 1 4 2 3 1 2 4 3 1 2 1 3 4 2 1 3 2 4 1 3 2 1 4 3 2 1 1 2 3 4 2 3 4 1 3 4 1 2 4 1 2 3 2 3 1 4 3 1 4 2 1 4 2 3 4 2 3 1 3 1 2 4 1 2 4 3 2 4 3 1 4 3 1 2 2 1 3 4 1 3 4 2 3 4 2 1 4 2 1 3 1 3 2 4 3 2 4 1 2 4 1 3 4 1 3 2 3 2 1 4 2 1 4 3 1 4 3 2 4 3 2 1 5! number of permutations of 1, 2, 3, 4, 5 = 124 possible (1 2 3 4 5) (1 2 3 5 4) (1 2 4 3 5) (1 2 4 5 3) (1 2 5 3 4) (1 2 5 4 3) (1 3 2 4 5) (1 3 2 5 4) (1 3 4 2 5) (1 3 4 5 2) (1 3 5 2 4) (1 3 5 4 2) (1 4 2 3 5) (1 4 2 5 3) (1 4 3 2 5) (1 4 3 5 2) (1 4 5 2 3) (1 4 5 3 2) (1 5 2 3 4) (1 5 2 4 3) (1 5 3 2 4) (1 5 3 4 2) (1 5 4 2 3) (1 5 4 3 2) ... (5 3 1 2 4) (5 3 1 4 2) (5 3 2 1 4) (5 3 2 4 1) (5 3 4 1 2) (5 3 4 2 1) (5 4 1 2 3) (5 4 1 3 2) (5 4 2 1 3) (5 4 2 3 1) (5 4 3 1 2) (5 4 3 2 1) optimum super permutation 153 ? expect ... 1 2 3 4 5 1 2 3 4 1 5 2 3 4 1 ... 1 4 3 2 5 1 4 3 2 1 5 4 3 2 1 1 2 3 4 5 2 3 4 5 1 3 4 5 1 2 4 5 1 2 3 5 1 2 3 4 2 3 4 1 5 3 4 1 5 2 4 1 5 2 3 1 5 2 3 4 5 2 3 4 1 1 4 3 2 5 4 3 2 5 3 2 5 1 4 2 5 1 4 3 5 1 4 3 2 4 3 2 1 5 3 2 1 5 4 2 1 5 4 3 1 5 4 3 2 5 4 3 2 1 6! number of permutations of 1, 2, 3, 4, 5, 6 = 720 possible (1 2 3 4 5 6) (1 2 3 4 6 5) (1 2 3 5 4 6) (1 2 3 5 6 4) (1 2 3 6 4 5) (1 2 3 6 5 4) (1 2 4 3 5 6) (1 2 4 3 6 5) (1 2 4 5 3 6) (1 2 4 5 6 3) (1 2 4 6 3 5) (1 2 4 6 5 3) (1 2 5 3 4 6) (1 2 5 3 6 4) (1 2 5 4 3 6) ... (6 5 2 3 4 1) (6 5 2 4 1 3) (6 5 2 4 3 1) (6 5 3 1 2 4) (6 5 3 1 4 2) (6 5 3 2 1 4) (6 5 3 2 4 1) (6 5 3 4 1 2) (6 5 3 4 2 1) (6 5 4 1 2 3) (6 5 4 1 3 2) (6 5 4 2 1 3) (6 5 4 2 3 1) (6 5 4 3 1 2) (6 5 4 3 2 1) optimum super permutation 872 expect ... 1 2 3 4 5 6 1 2 3 4 5 1 6 2 3 ... 2 6 1 5 4 3 2 1 6 5 4 3 2 1 1 2 3 4 5 6 2 3 4 5 6 1 3 4 5 6 1 2 4 5 6 1 2 3 5 6 1 2 3 4 6 1 2 3 4 5 3 4 5 1 6 2 4 5 1 6 2 3 ... 2 6 1 5 4 3 6 1 5 4 3 2 5 4 3 2 1 6 4 3 2 1 6 5 3 2 1 6 5 4 2 1 6 5 4 3 1 6 5 4 3 2 6 5 4 3 2 1 41! number of permutations of 1, 2, 3, ... ,41 = 87178291200 possible (1 2 3 4 5 6 7 8 9 10 11 12 13 14) ... (14 13 12 11 10 9 8 7 6 5 4 3 2 1) optimum super permutation ??? big math question User your mathmagical thinking to devise an algorithm, that does not involve searching, to generate super permutations.