96 lines
1.9 KiB
Plaintext
96 lines
1.9 KiB
Plaintext
{
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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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"# Powerful digit sum (Euler Problem 56)"
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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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"A googol ($10^{100}$) is a massive number: one followed by one-hundred zeros; $100^{100}$ is almost unimaginably large: one followed by two-hundred zeros. Despite their size, the sum of the digits in each number is only 1.\n",
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"\n",
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"Considering natural numbers of the form, $a^b$, where $a, b < 100$, what is the maximum digital sum?"
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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": 1,
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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 get_digit_sum(n):\n",
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" s = 0\n",
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" while n != 0:\n",
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" s += (n % 10)\n",
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" n //= 10\n",
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" return s\n",
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"\n",
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"assert(get_digit_sum(1337) == 14)\n",
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"assert(get_digit_sum(100**100) == 1)"
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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": 2,
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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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"972\n"
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]
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}
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],
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"source": [
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"s = max([get_digit_sum(a**b) for a in range(1, 100) for b in range(1, 100)])\n",
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"print(s)\n",
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"assert(s == 972)"
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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": "Mon, 24 Dec 2018, 23:33",
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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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"power",
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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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