2018-10-10 18:03:03 -04:00
---
id: 5900f5411000cf542c510053
2021-02-06 04:42:36 +00:00
title: 'Problem 469: Empty chairs'
2018-10-10 18:03:03 -04:00
challengeType: 5
2021-02-06 04:42:36 +00:00
forumTopicId: 302144
2021-01-13 03:31:00 +01:00
dashedName: problem-469-empty-chairs
2018-10-10 18:03:03 -04:00
---
2020-12-16 00:37:30 -07:00
# --description--
2018-10-10 18:03:03 -04:00
2021-02-06 04:42:36 +00:00
In a room N chairs are placed around a round table.
2018-10-10 18:03:03 -04:00
2021-02-06 04:42:36 +00:00
Knights enter the room one by one and choose at random an available empty chair.
2018-10-10 18:03:03 -04:00
2021-02-06 04:42:36 +00:00
To have enough elbow room the knights always leave at least one empty chair between each other.
When there aren't any suitable chairs left, the fraction C of empty chairs is determined. We also define E(N) as the expected value of C. We can verify that E(4) = 1/2 and E(6) = 5/9.
Find E(1018). Give your answer rounded to fourteen decimal places in the form 0.abcdefghijklmn.
2018-10-10 18:03:03 -04:00
2020-12-16 00:37:30 -07:00
# --hints--
2018-10-10 18:03:03 -04:00
2021-02-06 04:42:36 +00:00
`euler469()` should return 0.56766764161831.
2018-10-10 18:03:03 -04:00
```js
2020-12-16 00:37:30 -07:00
assert.strictEqual(euler469(), 0.56766764161831);
2018-10-10 18:03:03 -04:00
```
2021-01-13 03:31:00 +01:00
# --seed--
## --seed-contents--
```js
function euler469() {
return true;
}
euler469();
```
2020-12-16 00:37:30 -07:00
# --solutions--
2020-08-13 17:24:35 +02:00
2021-01-13 03:31:00 +01:00
```js
// solution required
```