statement.html
problem 55 · 14 lines
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<p>If we take $47$, reverse and add, $47 + 74 = 121$, which is palindromic.</p>
<p>Not all numbers produce palindromes so quickly. For example,</p>
$$\begin{align}
349 + 943 &= 1292\\
1292 + 2921 &= 4213\\
4213 + 3124 &= 7337
\end{align}$$
<p>That is, $349$ took three iterations to arrive at a palindrome.</p>
<p>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).</p>
<p>Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first example is $4994$.</p>
<p>How many Lychrel numbers are there below ten-thousand?</p>
<p class="smaller">NOTE: Wording was modified slightly on 24 April 2007 to emphasise the theoretical nature of Lychrel numbers.</p>
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