Decoding '_Brilliant_' Permutations

Solution with Python: import itertools

lst = list(itertools.permutations('BRILLIANT'))
lst.sort()

newLst = [lst[0], ]
for i in lst[1:]:
    if newLst[-1] != i:
        newLst.append(i)

print newLst.index(('A', 'B', 'R', 'L', 'L', 'I', 'T', 'N', 'I')) + 1

>>> 990

First consider ordering the letters of the word 'BRILLIANT'. That gives us the string 'ABIILLNRT' , which is the first possible permutation in lexicographic order.

There are 362880 actual possible permutations but not all of them are unique. Consider using 'Sets' (mathematically a set cannot contain duplicates) to store all possible permutations in lexicographic order. Obviously you 'll find that the string 'ABRLLITNI' is at position 990 !