67 lines
2.2 KiB
Markdown
67 lines
2.2 KiB
Markdown
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---
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id: 5900f54c1000cf542c51005f
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title: 'Problem 480: The Last Question'
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challengeType: 5
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forumTopicId: 302158
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dashedName: problem-480-the-last-question
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---
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# --description--
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Consider all the words which can be formed by selecting letters, in any order, from the phrase:
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$$\mathbf{\text{thereisasyetinsufficientdataforameaningfulanswer}}$$
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Suppose those with 15 letters or less are listed in alphabetical order and numbered sequentially starting at 1.
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The list would include:
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$$\begin{align} & 1: \text{a} \\\\ & 2: \text{aa} \\\\ & 3: \text{aaa} \\\\ & 4: \text{aaaa} \\\\ & 5: \text{aaaaa} \\\\ & 6: \text{aaaaaa} \\\\ & 7: \text{aaaaaac} \\\\ & 8: \text{aaaaaacd} \\\\ & 9: \text{aaaaaacde} \\\\ & 10: \text{aaaaaacdee} \\\\ & 11: \text{aaaaaacdeee} \\\\ & 12: \text{aaaaaacdeeee} \\\\ & 13: \text{aaaaaacdeeeee} \\\\ & 14: \text{aaaaaacdeeeeee} \\\\ & 15: \text{aaaaaacdeeeeeef} \\\\ & 16: \text{aaaaaacdeeeeeeg} \\\\ & 17: \text{aaaaaacdeeeeeeh} \\\\ & \ldots \\\\ & 28: \text{aaaaaacdeeeeeey} \\\\ & 29: \text{aaaaaacdeeeeef} \\\\ & 30: \text{aaaaaacdeeeeefe} \\\\ & \ldots \\\\ & 115246685191495242: \text{euleoywuttttsss} \\\\ & 115246685191495243: \text{euler} \\\\ & 115246685191495244: \text{eulera} \\\\ & ... \\\\ & 525069350231428029: \text{ywuuttttssssrrr} \\\\ \end{align}$$
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Define $P(w)$ as the position of the word $w$.
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Define $W(p)$ as the word in position $p$.
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We can see that $P(w)$ and $W(p)$ are inverses: $P(W(p)) = p$ and $W(P(w)) = w$.
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Examples:
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$$\begin{align} & W(10) = \text{ aaaaaacdee} \\\\ & P(\text{aaaaaacdee}) = 10 \\\\ & W(115246685191495243) = \text{ euler} \\\\ & P(\text{euler}) = 115246685191495243 \\\\ \end{align}$$
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Find $$W(P(\text{legionary}) + P(\text{calorimeters}) - P(\text{annihilate}) + P(\text{orchestrated}) - P(\text{fluttering})).$$
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Give your answer using lowercase characters (no punctuation or space).
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# --hints--
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`euler480()` should return a string.
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```js
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assert(typeof euler480() === 'string');
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```
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`euler480()` should return the string `turnthestarson`.
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```js
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assert.strictEqual(euler480(), 'turnthestarson');
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```
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# --seed--
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## --seed-contents--
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```js
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function euler480() {
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return true;
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}
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euler480();
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```
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# --solutions--
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```js
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// solution required
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```
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