# Problem 480: The Last Question
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: ywuuttttssssrrrDefine 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) =
115246685191495243Find W(P(legionary) + P(calorimeters) - P(annihilate)
+ P(orchestrated) - P(fluttering)). Give your answer using lowercase
characters (no punctuation or space).