62 lines
2.2 KiB
Markdown
62 lines
2.2 KiB
Markdown
|
---
|
|||
|
|
id: 5900f3a11000cf542c50feb4
|
|||
|
|
challengeType: 5
|
|||
|
|
title: 'Problem 53: Combinatoric selections'
|
|||
|
|
videoUrl: ''
|
|||
|
|
localeTitle: 'Проблема 53: Комбинаторный выбор'
|
|||
|
|
---
|
|||
|
|
|
|||
|
|
## Description
|
|||
|
|
<section id="description"> Существует ровно десять способов выбора трех из пяти, 12345: 123, 124, 125, 134, 135, 145, 234, 235, 245 и 345. В комбинаторике мы используем обозначение 5C3 = 10. В общем, <p> nCr = n! r! (n-r)! , где r ≤ n, n! = n × (n-1) × ... × 3 × 2 × 1 и 0! = 1. </p><p> Только до n = 23 значение превышает один миллион: 23C10 = 1144066. Сколько, не обязательно различных значений nCr для 1 ≤ n ≤ 100, превышает один миллион? </p></section>
|
|||
|
|
|
|||
|
|
## Instructions
|
|||
|
|
<section id="instructions">
|
|||
|
|
</section>
|
|||
|
|
|
|||
|
|
## Tests
|
|||
|
|
<section id='tests'>
|
|||
|
|
|
|||
|
|
```yml
|
|||
|
|
tests:
|
|||
|
|
- text: <code>combinatoricSelections(1000)</code> должен возвращать 4626.
|
|||
|
|
testString: 'assert.strictEqual(combinatoricSelections(1000), 4626, "<code>combinatoricSelections(1000)</code> should return 4626.");'
|
|||
|
|
- text: <code>combinatoricSelections(10000)</code> должен возвращать 4431.
|
|||
|
|
testString: 'assert.strictEqual(combinatoricSelections(10000), 4431, "<code>combinatoricSelections(10000)</code> should return 4431.");'
|
|||
|
|
- text: <code>combinatoricSelections(100000)</code> должен возвращать 4255.
|
|||
|
|
testString: 'assert.strictEqual(combinatoricSelections(100000), 4255, "<code>combinatoricSelections(100000)</code> should return 4255.");'
|
|||
|
|
- text: <code>combinatoricSelections(1000000)</code> должен возвращать 4075.
|
|||
|
|
testString: 'assert.strictEqual(combinatoricSelections(1000000), 4075, "<code>combinatoricSelections(1000000)</code> should return 4075.");'
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
</section>
|
|||
|
|
|
|||
|
|
## Challenge Seed
|
|||
|
|
<section id='challengeSeed'>
|
|||
|
|
|
|||
|
|
<div id='js-seed'>
|
|||
|
|
|
|||
|
|
```js
|
|||
|
|
function combinatoricSelections(limit) {
|
|||
|
|
// Good luck!
|
|||
|
|
return 1;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
combinatoricSelections(1000000);
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
</div>
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
</section>
|
|||
|
|
|
|||
|
|
## Solution
|
|||
|
|
<section id='solution'>
|
|||
|
|
|
|||
|
|
```js
|
|||
|
|
// solution required
|
|||
|
|
```
|
|||
|
|
</section>
|