75 lines
1.9 KiB
Plaintext
75 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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"id": "004a4666",
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"metadata": {},
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"source": [
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"# [Pandigital Products](https://projecteuler.net/problem=32)\n",
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"\n",
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"The product of any number with a four digit number will be at least four digits, meaning it is possible the multiplicand, multiplier, and product are pandigital, since there would be at least nine total digits. In contrast, the product of any number and a five digit number will be at least five digits, so the three-number combo will not be pandigital - it will have at least 11 digits.\n",
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"\n",
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"This allows to set bounds on our brute force. We will make sure neither factor is more than four digits."
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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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"id": "5d61d14d",
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"metadata": {},
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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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"def is_pandigital(n):\n",
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" return ''.join(sorted(n)) == \"123456789\"\n",
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"\n",
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"\n",
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"products = set()\n",
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"for p in range(1, 10000):\n",
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" for q in range(p, 10000):\n",
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" product = p * q\n",
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" \n",
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" s = f\"{p}{q}{product}\"\n",
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" if len(s) > 9:\n",
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" break\n",
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" \n",
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" if is_pandigital(s):\n",
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" products.add(product)\n",
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"\n",
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"sum(products)"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "SageMath 9.5",
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"language": "sage",
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"name": "sagemath"
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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": "3.11.2"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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