Added problems till 60 to ipynb.
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ipython/EulerProblem055.ipynb
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72
ipython/EulerProblem055.ipynb
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Lychrel numbers (Euler Problem 55)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"collapsed": true
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},
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"source": [
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"[https://projecteuler.net/problem=55](https://projecteuler.net/problem=55)\n",
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"\n",
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"If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.\n",
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"\n",
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"Not all numbers produce palindromes so quickly. For example,\n",
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"\n",
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"$349 + 943 = 1292$\n",
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"\n",
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"$1292 + 2921 = 4213$\n",
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"\n",
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"$4213 + 3124 = 7337$\n",
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"\n",
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"That is, 349 took three iterations to arrive at a palindrome.\n",
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"\n",
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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).\n",
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"\n",
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"Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first example is 4994.\n",
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"\n",
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"How many Lychrel numbers are there below ten-thousand?\n",
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"\n",
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"NOTE: Wording was modified slightly on 24 April 2007 to emphasise the theoretical nature of Lychrel numbers."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"completion_date": "",
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python3.6",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.6.5"
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},
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"tags": []
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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