79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
63 lines
1.4 KiB
Markdown
63 lines
1.4 KiB
Markdown
---
|
|
id: 5900f4071000cf542c50ff19
|
|
challengeType: 5
|
|
title: 'Problem 154: Exploring Pascal''s pyramid'
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
A triangular pyramid is constructed using spherical balls so that each ball rests on exactly three balls of the next lower level.
|
|
|
|
Then, we calculate the number of paths leading from the apex to each position:
|
|
A path starts at the apex and progresses downwards to any of the three spheres directly below the current position.
|
|
Consequently, the number of paths to reach a certain position is the sum of the numbers immediately above it (depending on the position, there are up to three numbers above it).
|
|
The result is Pascal's pyramid and the numbers at each level n are the coefficients of the trinomial expansion
|
|
(x + y + z)n.
|
|
How many coefficients in the expansion of (x + y + z)200000 are multiples of 1012?
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>euler154()</code> should return 479742450.
|
|
testString: assert.strictEqual(euler154(), 479742450, '<code>euler154()</code> should return 479742450.');
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function euler154() {
|
|
// Good luck!
|
|
return true;
|
|
}
|
|
|
|
euler154();
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
```js
|
|
// solution required
|
|
```
|
|
</section>
|