The 7 unique letters of the word PERPLEXUS are permuted in all possible ways and then the new “words” are listed alphabetically.

What "word" is at position 2020 in this list? .

(In reply to soln? by Steven Lord)

I took a non-computer programming approach using factorial values iterated to the sum of 2019 for use in the sorting. (The initial iteration being the 0th iteration; the 2020th, then being 2020 - 1 = 2019).

6!=720; 5!=120; 4!=24; 3!=6; 2!=2; 1!=1;
2×6! + 4×5! + 4×4! + 0×3! + 1×2! + 1×1! = 2019.

I, too, arranged the unique letters alphabetically [ELPRSUX : the first "word" of the permuted list], then rotating the digit columns like a combination lock using the value of the multiplicands [2,4,4,0,1,1,0], bypassing already set letters in the count, I arrived at the "word": PUXERSL.

Edited on August 24, 2020, 8:13 pm

Posted by Dej Mar on 2020-08-23 20:50:51