67 lines
1.2 KiB
Markdown
67 lines
1.2 KiB
Markdown
---
|
||
id: 5900f5091000cf542c51001b
|
||
challengeType: 5
|
||
title: 'Problem 408: Admissible paths through a grid'
|
||
forumTopicId: 302076
|
||
---
|
||
|
||
## Description
|
||
<section id='description'>
|
||
Let's call a lattice point (x, y) inadmissible if x, y and x + y are all positive perfect squares.
|
||
For example, (9, 16) is inadmissible, while (0, 4), (3, 1) and (9, 4) are not.
|
||
|
||
Consider a path from point (x1, y1) to point (x2, y2) using only unit steps north or east.
|
||
Let's call such a path admissible if none of its intermediate points are inadmissible.
|
||
|
||
Let P(n) be the number of admissible paths from (0, 0) to (n, n).
|
||
It can be verified that P(5) = 252, P(16) = 596994440 and P(1000) mod 1 000 000 007 = 341920854.
|
||
|
||
Find P(10 000 000) mod 1 000 000 007.
|
||
</section>
|
||
|
||
## Instructions
|
||
<section id='instructions'>
|
||
|
||
</section>
|
||
|
||
## Tests
|
||
<section id='tests'>
|
||
|
||
```yml
|
||
tests:
|
||
- text: <code>euler408()</code> should return 299742733.
|
||
testString: assert.strictEqual(euler408(), 299742733);
|
||
|
||
```
|
||
|
||
</section>
|
||
|
||
## Challenge Seed
|
||
<section id='challengeSeed'>
|
||
|
||
<div id='js-seed'>
|
||
|
||
```js
|
||
function euler408() {
|
||
// Good luck!
|
||
return true;
|
||
}
|
||
|
||
euler408();
|
||
```
|
||
|
||
</div>
|
||
|
||
|
||
|
||
</section>
|
||
|
||
## Solution
|
||
<section id='solution'>
|
||
|
||
```js
|
||
// solution required
|
||
```
|
||
|
||
</section>
|