115 lines
2.6 KiB
Plaintext
115 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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"id": "67a42435",
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"metadata": {},
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"source": [
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"# [Coded Triangle Numbers](https://projecteuler.net/problem=42)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "94f69404",
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"metadata": {},
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"source": [
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"First we read in the words:"
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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": "8d7380ba",
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"metadata": {},
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"outputs": [],
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"source": [
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"with open(\"txt/0042_words.txt\") as f:\n",
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" words = {w.strip('\"') for w in f.read().split(\",\")}"
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]
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},
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{
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"cell_type": "markdown",
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"id": "0a73cc47",
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"metadata": {},
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"source": [
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"We'll also write a simple function for testing if a word is a \"triangle word\". We'll make use of SageMath's built-in function for testing if a number is triangular."
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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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"id": "313a760f",
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"metadata": {},
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"outputs": [],
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"source": [
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"def is_triangle_word(word):\n",
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" value = sum(ord(c) - ord('A') + 1 for c in word)\n",
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" return is_triangular_number(value)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "ba53d2b1",
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"metadata": {},
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"source": [
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"(It's not difficult to apply the quadratic formula to write our own test for [triangular numbers](https://en.wikipedia.org/wiki/Triangular_number).)\n",
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"\n",
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"Now we just test each word."
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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": 3,
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"id": "14a9ea9a",
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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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"162"
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]
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},
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"execution_count": 3,
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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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"triangle_words = {w for w in words if is_triangle_word(w)}\n",
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"len(triangle_words)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "02bf08bf",
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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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