107 lines
2.2 KiB
Plaintext
107 lines
2.2 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 counts (Euler Problem 63)"
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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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"The 5-digit number, 16807=$7^5$, is also a fifth power. Similarly, the 9-digit number, 134217728=$8^9$, is a ninth power.\n",
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"\n",
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"How many n-digit positive integers exist which are also an nth power?"
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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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"outputs": [],
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"source": [
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"def get_digit_count(n):\n",
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" if n < 10:\n",
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" return 1\n",
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" c = 0\n",
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" while n:\n",
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" n //= 10\n",
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" c += 1\n",
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" return c\n",
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"\n",
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"assert(get_digit_count(0) == 1)\n",
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"assert(get_digit_count(1) == 1)\n",
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"assert(get_digit_count(33) == 2)\n",
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"assert(get_digit_count(100) == 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": 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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"49\n"
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]
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}
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],
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"source": [
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"def get_n_digit_positive_integers(n):\n",
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" r = []\n",
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" i = 1\n",
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" while True:\n",
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" if get_digit_count(i ** n) == n:\n",
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" r.append(i ** n)\n",
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" if get_digit_count(i ** n) > n:\n",
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" return r\n",
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" i += 1\n",
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"\n",
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"s = sum([len(get_n_digit_positive_integers(n)) for n in range(1, 1000)])\n",
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"print(s)\n",
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"assert(s == 49)"
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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, 6 Jan 2019, 06:17",
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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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"powers"
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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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