43 lines
846 B
Markdown
43 lines
846 B
Markdown
|
---
|
||
|
|
id: 5900f4de1000cf542c50fff0
|
||
|
|
title: 'Problem 369: Badugi'
|
||
|
|
challengeType: 5
|
||
|
|
forumTopicId: 302030
|
||
|
|
dashedName: problem-369-badugi
|
||
|
|
---
|
||
|
|
|
||
|
|
# --description--
|
||
|
|
|
||
|
|
In a standard 52 card deck of playing cards, a set of 4 cards is a Badugi if it contains 4 cards with no pairs and no two cards of the same suit.
|
||
|
|
|
||
|
|
Let f(n) be the number of ways to choose n cards with a 4 card subset that is a Badugi. For example, there are 2598960 ways to choose five cards from a standard 52 card deck, of which 514800 contain a 4 card subset that is a Badugi, so f(5) = 514800.
|
||
|
|
|
||
|
|
Find ∑f(n) for 4 ≤ n ≤ 13.
|
||
|
|
|
||
|
|
# --hints--
|
||
|
|
|
||
|
|
`euler369()` should return 862400558448.
|
||
|
|
|
||
|
|
```js
|
||
|
|
assert.strictEqual(euler369(), 862400558448);
|
||
|
|
```
|
||
|
|
|
||
|
|
# --seed--
|
||
|
|
|
||
|
|
## --seed-contents--
|
||
|
|
|
||
|
|
```js
|
||
|
|
function euler369() {
|
||
|
|
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
|
||
|
|
euler369();
|
||
|
|
```
|
||
|
|
|
||
|
|
# --solutions--
|
||
|
|
|
||
|
|
```js
|
||
|
|
// solution required
|
||
|
|
```
|