---
id: 5900f4f71000cf542c510009
title: '问题 394：吃馅饼'
challengeType: 1
forumTopicId: 302059
dashedName: problem-394-eating-pie
---

# --description--

杰夫以一种不同寻常的方式吃馅饼。

馅饼是圆形的。 他首先沿着半径切割馅饼中的初始切口。

While there is at least a given fraction $F$ of pie left, he performs the following procedure:

- He makes two slices from the pie centre to any point of what is remaining of the pie border, any point on the remaining pie border equally likely. This will divide the remaining pie into three pieces.
- Going counterclockwise from the initial cut, he takes the first two pie pieces and eats them.

When less than a fraction $F$ of pie remains, he does not repeat this procedure. Instead, he eats all of the remaining pie.

<img class="img-responsive center-block" alt="animation of pie slicing procedure" src="https://cdn.freecodecamp.org/curriculum/project-euler/eating-pie.gif" style="background-color: white; padding: 10px;" />

For $x ≥ 1$, let $E(x)$ be the expected number of times Jeff repeats the procedure above with $F = \frac{1}{x}$. It can be verified that $E(1) = 1$, $E(2) ≈ 1.2676536759$, and $E(7.5) ≈ 2.1215732071$.

Find $E(40)$ rounded to 10 decimal places behind the decimal point.

# --hints--

`eatingPie()` should return `3.2370342194`.

```js
assert.strictEqual(eatingPie(), 3.2370342194);
```

# --seed--

## --seed-contents--

```js
function eatingPie() {

  return true;
}

eatingPie();
```

# --solutions--

```js
// solution required
```
