chore(i8n,learn): processed translations
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Mrugesh Mohapatra
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---
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id: 5900f3a31000cf542c50feb6
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title: 问题55:Lychrel数字
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title: 'Problem 55: Lychrel numbers'
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challengeType: 5
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videoUrl: ''
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forumTopicId: 302166
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dashedName: problem-55-lychrel-numbers
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---
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# --description--
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如果我们采取47,反向并添加,47 + 74 = 121,这是回文。并非所有数字都如此迅速地产生回文。例如,349 + 943 = 1292,1292 + 2921 = 4213 4213 + 3124 = 7337也就是说,349进行了三次迭代以到达回文。虽然还没有人证明这一点,但据认为有些数字,如196,从未产生回文。通过反向和添加过程从不形成回文的数字称为Lychrel数。由于这些数字的理论性质,并且出于这个问题的目的,我们将假设一个数字是Lychrel,直到证明不是这样。另外,对于每万个低于一万的数字,你将得到(i)在不到五十次迭代中成为回文,或者(ii)没有一个,具有所有存在的计算能力,到目前为止已经管理到将它映射到回文结构。事实上,10677是第一个在产生回文之前需要超过50次迭代的数字:4668731596684224866951378664(53次迭代,28位数)。令人惊讶的是,有一些回文数字本身就是Lychrel数字;第一个例子是4994.有多少Lychrel数字在`num`以下?注:2007年4月24日略微修改了措辞,以强调Lychrel数的理论性质。
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If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.
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Not all numbers produce palindromes so quickly. For example,
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<div style="margin-left: 4em;">
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349 + 943 = 1292,<br>
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1292 + 2921 = 4213<br>
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4213 + 3124 = 7337<br>
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</div>
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That is, 349 took three iterations to arrive at a palindrome.
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Although no one has proved it yet, it is thought that some numbers, like 196, never produce a palindrome. A number that never forms a palindrome through the reverse and add process is called a Lychrel number. Due to the theoretical nature of these numbers, and for the purpose of this problem, we shall assume that a number is Lychrel until proven otherwise. In addition you are given that for every number below ten-thousand, it will either (i) become a palindrome in less than fifty iterations, or, (ii) no one, with all the computing power that exists, has managed so far to map it to a palindrome. In fact, 10677 is the first number to be shown to require over fifty iterations before producing a palindrome: 4668731596684224866951378664 (53 iterations, 28-digits).
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Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first example is 4994.
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How many Lychrel numbers are there below `num`?
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**Note:** Wording was modified slightly on 24 April 2007 to emphasize the theoretical nature of Lychrel numbers.
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# --hints--
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`countLychrelNumbers(1000)`应该返回13。
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`countLychrelNumbers(1000)` should return a number.
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```js
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assert(typeof countLychrelNumbers(1000) === 'number');
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```
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`countLychrelNumbers(1000)` should return 13.
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```js
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assert.strictEqual(countLychrelNumbers(1000), 13);
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```
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`countLychrelNumbers(5000)`应该返回76。
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```js
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assert.strictEqual(countLychrelNumbers(5000), 76);
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```
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`countLychrelNumbers(10000)`应该返回249。
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```js
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assert.strictEqual(countLychrelNumbers(10000), 249);
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```
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你的函数应该计算所有Lychrel数。
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`countLychrelNumbers(3243)` should return 39.
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```js
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assert.strictEqual(countLychrelNumbers(3243), 39);
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```
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您的函数应该通过所有测试用例。
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`countLychrelNumbers(5000)` should return 76.
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```js
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assert.strictEqual(countLychrelNumbers(5000), 76);
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```
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`countLychrelNumbers(7654)` should return 140.
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```js
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assert.strictEqual(countLychrelNumbers(7654), 140);
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```
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`countLychrelNumbers(10000)` should return 249.
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```js
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assert.strictEqual(countLychrelNumbers(10000), 249);
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```
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# --seed--
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## --seed-contents--
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