add problem 33

notebooks/problem0033.ipynb

@@ -0,0 +1,128 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "eb246b50",
+   "metadata": {},
+   "source": [
+    "# [Digit Cancelling Fractions](https://projecteuler.net/problem=33)\n",
+    "\n",
+    "The search term for this concept is an [anomalous cancellation](https://en.wikipedia.org/wiki/Anomalous_cancellation). We can write a function that checks if an anomalous cancellation can happen by storing the digits of the numerator and denominator into four variables total, then checking four separate cases for if a digit can be \"cancelled.\""
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "d4e94963",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def digits(n):\n",
+    "    return (n // 10, n % 10)\n",
+    "\n",
+    "\n",
+    "def can_cancel_digits(n, d):\n",
+    "    x, y = digits(n)\n",
+    "    z, w = digits(d)\n",
+    "\n",
+    "    f = QQ(n/d)\n",
+    "\n",
+    "    if x == z and w != 0 and y/w == f:\n",
+    "        return True\n",
+    "    elif x == w and y/z == f:\n",
+    "        return True\n",
+    "    elif y == z and w != 0 and x/w == f:\n",
+    "        return True\n",
+    "    elif y == w and w != 0 and x/z == f:\n",
+    "        return True\n",
+    "\n",
+    "    return False"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a68309e9",
+   "metadata": {},
+   "source": [
+    "We're only dealing with two-digit numerators and denominators, so this is easy to brute force."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "756614f7",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{(16, 64), (19, 95), (26, 65), (49, 98)}"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "fractions = set()\n",
+    "for n in range(10, 100):\n",
+    "    for d in range(n + 1, 100):\n",
+    "        if can_cancel_digits(n, d):\n",
+    "            fractions.add((n, d))\n",
+    "\n",
+    "fractions"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6d3fb43b",
+   "metadata": {},
+   "source": [
+    "There's only four such fractions."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "90f47a7f",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "100"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "prod(QQ(n/d) for (n, d) in fractions).denominator()"
+   ]
+  }
+ ],
+ "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
+}