84 lines
1.9 KiB
Plaintext
84 lines
1.9 KiB
Plaintext
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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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"# Euler Problem 30\n",
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"\n",
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"Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits:\n",
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"\n",
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"$1634 = 1^4 + 6^4 + 3^4 + 4^4$\n",
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"\n",
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"$8208 = 8^4 + 2^4 + 0^4 + 8^4$\n",
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"\n",
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"$9474 = 9^4 + 4^4 + 7^4 + 4^4$\n",
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"\n",
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"As $1 = 1^4$ is not a sum it is not included.\n",
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"\n",
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"The sum of these numbers is $1634 + 8208 + 9474 = 19316$.\n",
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"\n",
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"Find the sum of all the numbers that can be written as the sum of fifth powers of their digits."
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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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"This is an eays brute force. We look up the fifth powers."
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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": 7,
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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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"443839\n"
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]
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}
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],
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"source": [
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"fifth_power_lookup = {str(i): i**5 for i in range(0,10)}\n",
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"\n",
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"def is_number_sum_of_fiths_powers_of_digits(n):\n",
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" return n == sum([fifth_power_lookup[d] for d in str(n)])\n",
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"\n",
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"s = sum([i for i in range(1, 1000000) if is_number_sum_of_fiths_powers_of_digits(i) and not i is 1])\n",
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"print(s)\n",
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"assert(s == 443839)"
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]
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}
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],
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"metadata": {
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"completion_date": "Fri, 25 Aug 2017, 12:13",
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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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": "3.6.3"
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},
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"tags": [
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"digit",
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"powers",
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"brute force"
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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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