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---
id: 5900f3a31000cf542c50feb6
title: 问题55Lychrel数字
title: 'Problem 55: Lychrel numbers'
challengeType: 5
videoUrl: ''
forumTopicId: 302166
dashedName: problem-55-lychrel-numbers
---
# --description--
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466873159668422486695137866453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2007年4月24日略微修改了措辞以强调Lychrel数的理论性质。
If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.
Not all numbers produce palindromes so quickly. For example,
<div style="margin-left: 4em;">
349 + 943 = 1292,<br>
1292 + 2921 = 4213<br>
4213 + 3124 = 7337<br>
</div>
That is, 349 took three iterations to arrive at a palindrome.
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).
Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first example is 4994.
How many Lychrel numbers are there below `num`?
**Note:** Wording was modified slightly on 24 April 2007 to emphasize the theoretical nature of Lychrel numbers.
# --hints--
`countLychrelNumbers(1000)`应该返回13。
`countLychrelNumbers(1000)` should return a number.
```js
assert(typeof countLychrelNumbers(1000) === 'number');
```
`countLychrelNumbers(1000)` should return 13.
```js
assert.strictEqual(countLychrelNumbers(1000), 13);
```
`countLychrelNumbers(5000)`应该返回76。
```js
assert.strictEqual(countLychrelNumbers(5000), 76);
```
`countLychrelNumbers(10000)`应该返回249。
```js
assert.strictEqual(countLychrelNumbers(10000), 249);
```
你的函数应该计算所有Lychrel数。
`countLychrelNumbers(3243)` should return 39.
```js
assert.strictEqual(countLychrelNumbers(3243), 39);
```
您的函数应该通过所有测试用例。
`countLychrelNumbers(5000)` should return 76.
```js
assert.strictEqual(countLychrelNumbers(5000), 76);
```
`countLychrelNumbers(7654)` should return 140.
```js
assert.strictEqual(countLychrelNumbers(7654), 140);
```
`countLychrelNumbers(10000)` should return 249.
```js
assert.strictEqual(countLychrelNumbers(10000), 249);
```
# --seed--
## --seed-contents--