chore(i8n,learn): processed translations
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Mrugesh Mohapatra
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---
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id: 5900f4f71000cf542c510009
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title: 问题394:吃馅饼
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title: 'Problem 394: Eating pie'
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challengeType: 5
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videoUrl: ''
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forumTopicId: 302059
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dashedName: problem-394-eating-pie
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---
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# --description--
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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。虽然剩下至少给定的馅饼F分数,但他执行以下程序: - 他从饼图中心到馅饼边框剩余的任何一点做两个切片,剩下的馅饼边框上的任何一点都有可能。这将把剩下的馅饼分成三块。 - 从最初的切割逆时针走,他拿出前两个馅饼并吃掉它们。当剩下不到一小部分馅饼时,他不再重复这个过程。相反,他吃剩下的所有馅饼。
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Jeff eats a pie in an unusual way.
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对于x≥1,设E(x)是Jeff重复上述过程的预期次数,F = 1 / x。可以证实E(1)= 1,E(2)≈1.2676536759,和E(7.5)≈2.1215732071。
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The pie is circular. He starts with slicing an initial cut in the pie along a radius.
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找到E(40)舍入到小数点后面的10位小数。
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While there is at least a given fraction F of pie left, he performs the following procedure:
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\- 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.
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\- Going counterclockwise from the initial cut, he takes the first two pie pieces and eats them.
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When less than a fraction F of pie remains, he does not repeat this procedure. Instead, he eats all of the remaining pie.
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For x ≥ 1, let E(x) be the expected number of times Jeff repeats the procedure above with F = 1/x. It can be verified that E(1) = 1, E(2) ≈ 1.2676536759, and E(7.5) ≈ 2.1215732071.
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Find E(40) rounded to 10 decimal places behind the decimal point.
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# --hints--
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`euler394()`应返回3.2370342194。
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`euler394()` should return 3.2370342194.
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```js
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assert.strictEqual(euler394(), 3.2370342194);
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