Solved 49.
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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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"# Prime permutations (Euler Problem 49)"
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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=49](https://projecteuler.net/problem=49)\n",
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"\n",
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"The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.\n",
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"\n",
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"There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing sequence.\n",
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"\n",
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"What 12-digit number do you form by concatenating the three terms in this sequence?"
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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": 20,
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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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"def sieve_of_eratosthenes(number):\n",
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" primes = []\n",
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" prospects = [n for n in range(2, number)]\n",
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" while prospects:\n",
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" p = prospects[0]\n",
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" prospects = [x for x in prospects if x % p != 0]\n",
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" primes.append(p)\n",
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" if p * p > number:\n",
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" break\n",
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" return primes + prospects\n",
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"\n",
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"ps = [p for p in sieve_of_eratosthenes(10000) if p > 1000]"
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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": 21,
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"metadata": {},
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"outputs": [],
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"source": [
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"d = {}\n",
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"for p in ps:\n",
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" s = \"\".join(sorted(str(p)))\n",
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" try:\n",
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" d[s].append(p)\n",
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" except KeyError:\n",
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" d[s] = [p]\n",
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" \n",
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"pss = [value for key, value in d.items() if len(value) >= 3]"
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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": 48,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[[1487, 4817, 8147], [2969, 6299, 9629]]\n"
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]
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}
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],
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"source": [
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"def find_increasing_sequence(xs):\n",
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" deltas = [(xs[j] - xs[i], i, j)\n",
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" for i in range(0, len(xs) - 1)\n",
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" for j in range(i + 1, len(xs))\n",
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" ]\n",
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" d = {}\n",
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" for delta, i, j in deltas:\n",
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" if delta in d and d[delta][-1] == i:\n",
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" d[delta].append(j)\n",
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" else:\n",
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" d[delta] = [i, j]\n",
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" for delta, sequence in d.items():\n",
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" if len(sequence) == 3:\n",
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" return [xs[index] for index in sequence]\n",
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" return []\n",
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"\n",
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"s = [find_increasing_sequence(ps) for ps in pss if find_increasing_sequence(ps)]\n",
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"print(s)"
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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": 49,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"296962999629\n"
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]
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}
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],
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"source": [
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"s = int(\"\".join(map(str, s[1])))\n",
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"assert(s == 296962999629)\n",
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"print(s)"
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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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"source": [
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"Congratulations, the answer you gave to problem 49 is correct.\n",
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"\n",
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"You are the 49654th person to have solved this problem.\n",
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"\n",
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"Nice work, failx, you've just advanced to Level 2 . \n",
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"46903 members (5.43%) have made it this far.\n",
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"\n",
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"This problem had a difficulty rating of 5%. The highest difficulty rating you have solved remains at 5%. "
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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": "Sun, 23 Dec 2018, 01:10",
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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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"permutations",
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"primes",
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"sequence"
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]
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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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@ -775,6 +775,22 @@
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</tr>
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<tr>
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<td><a href="EulerProblem049.html">Problem 049</a></td>
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<td>Sun, 23 Dec 2018, 01:10</td>
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<td>
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<kbd>permutations</kbd>
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<kbd>primes</kbd>
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<kbd>sequence</kbd>
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</td>
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</tr>
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<tr>
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<td><a href="EulerProblem067.html">Problem 067</a></td>
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