projecteuler.net

The Last Question

Published on Sunday, 14th September 2014, 01:00 am; Solved by 450;
Difficulty rating: 45%

Problem 480

Consider all the words which can be formed by selecting letters, in any order, from the phrase:

thereisasyetinsufficientdataforameaningfulanswer

Suppose those with 15 letters or less are listed in alphabetical order and numbered sequentially starting at 1.
The list would include:

  • 1 : a
  • 2 : aa
  • 3 : aaa
  • 4 : aaaa
  • 5 : aaaaa
  • 6 : aaaaaa
  • 7 : aaaaaac
  • 8 : aaaaaacd
  • 9 : aaaaaacde
  • 10 : aaaaaacdee
  • 11 : aaaaaacdeee
  • 12 : aaaaaacdeeee
  • 13 : aaaaaacdeeeee
  • 14 : aaaaaacdeeeeee
  • 15 : aaaaaacdeeeeeef
  • 16 : aaaaaacdeeeeeeg
  • 17 : aaaaaacdeeeeeeh
  • ...
  • 28 : aaaaaacdeeeeeey
  • 29 : aaaaaacdeeeeef
  • 30 : aaaaaacdeeeeefe
  • ...
  • 115246685191495242: euleoywuttttsss
  • 115246685191495243: euler
  • 115246685191495244: eulera
  • ...
  • 525069350231428029: ywuuttttssssrrr

Define P(w) as the position of the word w.
Define W(p) as the word in position p.
We can see that P(w) and W(p) are inverses: P(W(p)) = p and W(P(w)) = w.

Examples:

  • W(10) = aaaaaacdee
  • P(aaaaaacdee) = 10
  • W(115246685191495243) = euler
  • P(euler) = 115246685191495243

Find W(P(legionary) + P(calorimeters) - P(annihilate) + P(orchestrated) - P(fluttering)).
Give your answer using lowercase characters (no punctuation or space).