2018-10-10 22:03:03 +00:00
---
id: 5900f5361000cf542c510049
2021-02-06 04:42:36 +00:00
title: 'Problem 458: Permutations of Project'
2018-10-10 22:03:03 +00:00
challengeType: 5
2021-02-06 04:42:36 +00:00
forumTopicId: 302132
2021-01-13 02:31:00 +00:00
dashedName: problem-458-permutations-of-project
2018-10-10 22:03:03 +00:00
---
2020-12-16 07:37:30 +00:00
# --description--
2018-10-10 22:03:03 +00:00
2021-02-06 04:42:36 +00:00
Consider the alphabet A made out of the letters of the word "project": A={c,e,j,o,p,r,t}.
2018-10-10 22:03:03 +00:00
2021-02-06 04:42:36 +00:00
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".
2018-10-10 22:03:03 +00:00
2021-02-06 04:42:36 +00:00
T(7)=77-7!=818503.
Find T(1012). Give the last 9 digits of your answer.
2018-10-10 22:03:03 +00:00
2020-12-16 07:37:30 +00:00
# --hints--
2018-10-10 22:03:03 +00:00
2021-02-06 04:42:36 +00:00
`euler458()` should return 423341841.
2018-10-10 22:03:03 +00:00
```js
2020-12-16 07:37:30 +00:00
assert.strictEqual(euler458(), 423341841);
2018-10-10 22:03:03 +00:00
```
2021-01-13 02:31:00 +00:00
# --seed--
## --seed-contents--
```js
function euler458() {
return true;
}
euler458();
```
2020-12-16 07:37:30 +00:00
# --solutions--
2020-08-13 15:24:35 +00:00
2021-01-13 02:31:00 +00:00
```js
// solution required
```