add problem 42

notebooks/problem0042.ipynb

@@ -0,0 +1,104 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "67a42435",
+   "metadata": {},
+   "source": [
+    "# [Coded Triangle Numbers](https://projecteuler.net/problem=42)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "94f69404",
+   "metadata": {},
+   "source": [
+    "First we read in the words:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "8d7380ba",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "with open(\"txt/0042_words.txt\") as f:\n",
+    "    words = {w.strip('\"') for w in f.read().split(\",\")}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0a73cc47",
+   "metadata": {},
+   "source": [
+    "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."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "313a760f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def is_triangle_word(word):\n",
+    "    value = sum(ord(c) - ord('A') + 1 for c in word)\n",
+    "    return is_triangular_number(value)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ba53d2b1",
+   "metadata": {},
+   "source": [
+    "(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",
+    "\n",
+    "Now we just test each word."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "14a9ea9a",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "162"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "triangle_words = {w for w in words if is_triangle_word(w)}\n",
+    "len(triangle_words)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "SageMath 9.5",
+   "language": "sage",
+   "name": "sagemath"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}