92 lines
2.6 KiB
Plaintext
92 lines
2.6 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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"# Euler Problem 32\n",
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"\n",
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"We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once; for example, the 5-digit number, 15234, is 1 through 5 pandigital.\n",
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"\n",
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"The product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital.\n",
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"\n",
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"Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through 9 pandigital.\n",
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"\n",
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"HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum."
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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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"We start by thinking about how many digits are used for multiplicand/multiplier/product. Obviously, the product must have more then three digits. Can it have more then 4 digits? Obviously it can because then there are only four digits for multiplicand and multiplier which is always smaller than ten thousand. So our product must be in the form $12 \\cdot 345 = 5789$. This makes the rest very easy in Python."
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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": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"45228"
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]
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},
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"execution_count": 1,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"from itertools import permutations\n",
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"\n",
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"def is_solution(s):\n",
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" a, b, c = int(s[0:2]), int(s[2:5]), int(s[5:])\n",
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" if a * b == c:\n",
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" return c\n",
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" a, b, c = int(s[0:1]), int(s[1:5]), int(s[5:]) \n",
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" if a * b == c:\n",
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" return c\n",
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" return 0\n",
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"\n",
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"assert(is_solution(\"391867254\") == 7254)\n",
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"assert(is_solution(\"391867245\") == 0)\n",
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"\n",
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"\n",
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"s = sum(set([is_solution(\"\".join(p)) for p in permutations(\"123456789\")]))\n",
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"assert(s == 45228)\n",
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"s"
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]
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}
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],
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"metadata": {
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"completion_date": "Wed, 30 Aug 2017, 14:25",
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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": "3.5.4"
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},
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"tags": [
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"pandigital",
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"products"
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]
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}
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