45 lines
857 B
Markdown
45 lines
857 B
Markdown
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---
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id: 5900f5361000cf542c510049
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title: 'Problem 458: Permutations of Project'
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challengeType: 5
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forumTopicId: 302132
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dashedName: problem-458-permutations-of-project
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---
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# --description--
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Consider the alphabet $A$ made out of the letters of the word `project`: $A = \\{c, e, j, o, p, r, t\\}$.
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Let $T(n)$ be the number of strings of length $n$ consisting of letters from $A$ that do not have a substring that is one of the 5040 permutations of `project`.
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$T(7) = 7^7 - 7! = 818\\,503$.
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Find $T({10}^{12})$. Give the last 9 digits of your answer.
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# --hints--
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`permutationsOfProject()` should return `423341841`.
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```js
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assert.strictEqual(permutationsOfProject(), 423341841);
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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 permutationsOfProject() {
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return true;
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}
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permutationsOfProject();
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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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