65 lines
1.5 KiB
Markdown
65 lines
1.5 KiB
Markdown
---
|
||
id: 5900f3ea1000cf542c50fefd
|
||
challengeType: 5
|
||
title: 'Problem 126: Cuboid layers'
|
||
forumTopicId: 301753
|
||
---
|
||
|
||
## Description
|
||
<section id='description'>
|
||
The minimum number of cubes to cover every visible face on a cuboid measuring 3 x 2 x 1 is twenty-two.
|
||
|
||
|
||
If we then add a second layer to this solid it would require forty-six cubes to cover every visible face, the third layer would require seventy-eight cubes, and the fourth layer would require one-hundred and eighteen cubes to cover every visible face.
|
||
However, the first layer on a cuboid measuring 5 x 1 x 1 also requires twenty-two cubes; similarly the first layer on cuboids measuring 5 x 3 x 1, 7 x 2 x 1, and 11 x 1 x 1 all contain forty-six cubes.
|
||
We shall define C(n) to represent the number of cuboids that contain n cubes in one of its layers. So C(22) = 2, C(46) = 4, C(78) = 5, and C(118) = 8.
|
||
It turns out that 154 is the least value of n for which C(n) = 10.
|
||
Find the least value of n for which C(n) = 1000.
|
||
</section>
|
||
|
||
## Instructions
|
||
<section id='instructions'>
|
||
|
||
</section>
|
||
|
||
## Tests
|
||
<section id='tests'>
|
||
|
||
```yml
|
||
tests:
|
||
- text: <code>euler126()</code> should return 18522.
|
||
testString: assert.strictEqual(euler126(), 18522);
|
||
|
||
```
|
||
|
||
</section>
|
||
|
||
## Challenge Seed
|
||
<section id='challengeSeed'>
|
||
|
||
<div id='js-seed'>
|
||
|
||
```js
|
||
function euler126() {
|
||
// Good luck!
|
||
return true;
|
||
}
|
||
|
||
euler126();
|
||
```
|
||
|
||
</div>
|
||
|
||
|
||
|
||
</section>
|
||
|
||
## Solution
|
||
<section id='solution'>
|
||
|
||
```js
|
||
// solution required
|
||
```
|
||
|
||
</section>
|