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Lychrel Numbers

I came across the below problem on Project Euler which is a fantastic website to practice and improve your coding skills by solving interesting challenges such as this:

If we take 47, reverse and add (47 + 74 = 121) it results in a palindrome.

Not all numbers produce palindromes so quickly. For example,

349 + 943 = 1292
1292 + 2921 = 4213
4213 + 3124 = 7337

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. You can assume that every number below ten-thousand 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).

How many Lychrel numbers are there below ten-thousand?

You are encouraged to attempt to solve the problem yourself. See the next page for a possible solution of this problem.

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