Problem 1082. Lychrel Number Test (Inspired by Project Euler Problem 55)

Created by @bmtran (Bryant Tran)

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The task for this problem is to create a function that takes a number n and tests if it might be a Lychrel number. This is, return <tt>true</tt> if the number satisfies the criteria stated below.From Project Euler: <a href="http://projecteuler.net/problem=55">Link</a>If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.Not all numbers produce palindromes so quickly. For example,349 + 943 = 1292,
1292 + 2921 = 4213
4213 + 3124 = 7337That 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.

The task for this problem is to create a function that takes a number _n_ and tests if it might be a Lychrel number. This is, return |true| if the number satisfies the criteria stated below.

*From Project Euler:* <http://projecteuler.net/problem=55 Link>

If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.

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. 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.

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265 Solutions
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Last Solution submitted on Jan 06, 2022

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Problem Comments

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bainhome on 6 Apr 2018

I think this assertion part is obsolete, in the form of "assert(islychrel(n))" or "assert(~islychrel(n))" now will fail directly on the new cody system. my code run at my computer seems fine by the way.

Tom Holz on 18 Aug 2018

It looks like there is an error in the test suite, because 3664 becomes 475574 after 5 iterations, although the test suite says that it's not a Lychrel number. (In addition, OEIS A023108, which lists all non-Lychrel numbers up to 3675, excludes 3664).

Rafael S.T. Vieira on 9 Aug 2020

Currently, the test suite seems to be working fine.

Nguyen Huy on 15 May 2021

Tom Holz cause you and me is misunderstood the problem,the problem is check number "not palindrome"

Solution Comments

Solution 172900

2 Comments

2 Comments

J.R.! Menzinger on 5 Dec 2012

ok! sorry for this, I missunderstood the problem... :-(

J.R.! Menzinger on 5 Dec 2012

my solution is here:
http://www.mathworks.com/matlabcentral/cody/problems/1082-lychrel-number-test-inspired-by-project-euler-problem-55/solutions/172901

So, I'M NOT LEADER IN THIS PROBLEM!

Solution 172599

1 Comment

1 Comment

J.R.! Menzinger on 5 Dec 2012

Sorry, you are leader... :-(

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