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 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
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19
9
the answer is 95
Total of 720 combinations:1 --- 12 --- 23 --- 64 --- 245 --- 1206 --- 7207 --- 5040.......Notice that:A --- BC --- DE --- FG --- XIn this sequence, if you wanted to know "X", it would be equal to FxG, and that is the key to this sequence. Why does it happen?Well, if, lets see, for instance, if 2 digits (0 and 1) have a possible of two combinations (10 and 01), then 3 digits (0, 1 and 2) will have a possible of six combinations: 012021And equivelent, but switching 0 with either 1 or 2, making it repeat itself 3 times.Eventually, we will end up doing 2 (number of combinations with 2 digits) times 3 (number of digits of which we want to know the number of unique combinations possible), totallizing 6 (our wanted-to-know number)
If each number can be used only once then there are just four: 2345, 2346, 2456 and 3456. There are no others because the order of the digits does not matter in combinations.