{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Coded triangle numbers (Euler Problem 42)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The nth term of the sequence of triangle numbers is given by, $t_n = \\frac{1}{2}n(n+1)$; so the first ten triangle numbers are:\n", "\n", " 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...\n", "\n", "By converting each letter in a word to a number corresponding to its alphabetical position and adding these values we form a word value. For example, the word value for SKY is 19 + 11 + 25 = 55 = $t_{10}$. If the word value is a triangle number then we shall call the word a triangle word.\n", "\n", "Using words.txt (right click and 'Save Link/Target As...'), a 16K text file containing nearly two-thousand common English words, how many are triangle words? (The file is saved in the same directory as this notebook file as EulerProblem042.txt)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "completion_date": "", "kernelspec": { "display_name": "Python 3", "language": "python3.6", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" }, "tags": [ "triangle", "words" ] }, "nbformat": 4, "nbformat_minor": 2 }