A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The lexicographic permutations of 0, 1 and 2 are:

012 021 102 120 201 210

What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?



In [11]:

    
import itertools

list(sorted(itertools.permutations(range(10))))[1000000-1]









    Out[11]:





(2, 7, 8, 3, 9, 1, 5, 4, 6, 0)



In [9]:

    
import math
math.factorial(10)









    Out[9]:





3628800



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