71 lines
1.7 KiB
Plaintext
71 lines
1.7 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "9c7a281d",
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"metadata": {},
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"source": [
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"# [Largest Palindrome Product](https://projecteuler.net/problem=4)\n",
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"\n",
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"Our search space is only $\\binom{900}{2} = 404550$ 3-digit pairs - a lot to check by hand but peanuts to a modern computer (we're using notation for [combinations](https://en.wikipedia.org/wiki/Combination) if you're unfamiliar)."
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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": "e5fd66f6",
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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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"906609"
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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 combinations\n",
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"\n",
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"is_palindrome = lambda x: str(x) == str(x)[::-1]\n",
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"three_digit_pairs = combinations(range(100, 1000), 2)\n",
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"max(x*y for (x,y) in three_digit_pairs if is_palindrome(x*y))"
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]
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},
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{
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"cell_type": "markdown",
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"id": "ac68b4da",
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"metadata": {},
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"source": [
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"#### Copyright (C) 2025 filifa\n",
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"\n",
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"This work is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International license](https://creativecommons.org/licenses/by-sa/4.0/) and the [BSD Zero Clause license](https://spdx.org/licenses/0BSD.html)."
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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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