22afc2a0ca
Co-authored-by: Oliver Eyton-Williams <ojeytonwilliams@gmail.com> Co-authored-by: Kristofer Koishigawa <scissorsneedfoodtoo@gmail.com> Co-authored-by: Beau Carnes <beaucarnes@gmail.com>
97 lines
2.3 KiB
Markdown
97 lines
2.3 KiB
Markdown
---
|
||
id: 5900f3a11000cf542c50feb4
|
||
challengeType: 5
|
||
isHidden: false
|
||
title: 'Problem 53: Combinatoric selections'
|
||
forumTopicId: 302164
|
||
---
|
||
|
||
## Description
|
||
<section id='description'>
|
||
|
||
There are exactly ten ways of selecting three from five, 12345:
|
||
|
||
<div style='text-align: center;'>123, 124, 125, 134, 135, 145, 234, 235, 245, and 345</div>
|
||
|
||
In combinatorics, we use the notation, $\displaystyle \binom 5 3 = 10$
|
||
|
||
In general, $\displaystyle \binom n r = \dfrac{n!}{r!(n-r)!}$, where $r \le n$, $n! = n \times (n-1) \times ... \times 3 \times 2 \times 1$, and $0! = 1$.
|
||
|
||
It is not until $n = 23$, that a value exceeds one-million: $\displaystyle \binom {23} {10} = 1144066$.
|
||
|
||
How many, not necessarily distinct, values of $\displaystyle \binom n r$ for $1 \le n \le 100$, are greater than one-million?
|
||
|
||
</section>
|
||
|
||
## Instructions
|
||
<section id='instructions'>
|
||
|
||
</section>
|
||
|
||
## Tests
|
||
<section id='tests'>
|
||
|
||
```yml
|
||
tests:
|
||
- text: <code>combinatoricSelections(1000)</code> should return a number.
|
||
testString: assert(typeof combinatoricSelections(1000) === 'number');
|
||
- text: <code>combinatoricSelections(1000)</code> should return 4626.
|
||
testString: assert.strictEqual(combinatoricSelections(1000), 4626);
|
||
- text: <code>combinatoricSelections(10000)</code> should return 4431.
|
||
testString: assert.strictEqual(combinatoricSelections(10000), 4431);
|
||
- text: <code>combinatoricSelections(100000)</code> should return 4255.
|
||
testString: assert.strictEqual(combinatoricSelections(100000), 4255);
|
||
- text: <code>combinatoricSelections(1000000)</code> should return 4075.
|
||
testString: assert.strictEqual(combinatoricSelections(1000000), 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
|
||
function combinatoricSelections(limit) {
|
||
const factorial = n =>
|
||
Array.apply(null, { length: n })
|
||
.map((_, i) => i + 1)
|
||
.reduce((p, c) => p * c, 1);
|
||
|
||
let result = 0;
|
||
const nMax = 100;
|
||
|
||
for (let n = 1; n <= nMax; n++) {
|
||
for (let r = 0; r <= n; r++) {
|
||
if (factorial(n) / (factorial(r) * factorial(n - r)) >= limit)
|
||
result++;
|
||
}
|
||
}
|
||
|
||
return result;
|
||
}
|
||
```
|
||
|
||
</section>
|