If all the 40320 (base 10) permutations of 12345678 in the hexadadecimal (base 16) representation are put in numerical order, what is the 20230th (base ten) pemutation?
This is basically the same task as
Millionth Pandigital II (and other problems) so I'll use the same method as I did there.
Offset 20230 by 1 to 20229, then converting 20229 to base factorial yields 20229 = 4002311_BF
Increment each digit by 1 gives the list {5,1,1,3,4,2,2}. Then remove without replacement that position from the sorted list {1,2,3,4,5,6,7,8}
The numbers removed are in order 5, 1, 2, 6, 8, 4, 7, with 3 remaining as the last number. String those together in order to get 51268473 as the 20230th ordered permutation of 12345678.
I don't know what hexadecimal has to do with anything in the problem.
Solution
