add problem 90

notebooks/problem0090.ipynb

@@ -0,0 +1,142 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "24453968",
+   "metadata": {},
+   "source": [
+    "# [Cube Digit Pairs](https://projecteuler.net/problem=90)\n",
+    "\n",
+    "There's only ${10 \\choose 6} = 210$ distinct cubes, making this problem easy to brute force. We first make a generator for those cubes."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "06b0661f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from itertools import combinations\n",
+    "\n",
+    "def cubes():\n",
+    "    yield from combinations(range(0, 10), 6)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "87ba05f8",
+   "metadata": {},
+   "source": [
+    "We also write a simple function for handling the fact that we can flip 6s and 9s."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "15dab5dd",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def extended_set(s):\n",
+    "    s = set(s)\n",
+    "    if 6 in s:\n",
+    "        s.add(9)\n",
+    "    elif 9 in s:\n",
+    "        s.add(6)\n",
+    "        \n",
+    "    return s"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "42f875d0",
+   "metadata": {},
+   "source": [
+    "Another simple function tests if we can display all the square numbers with a given pair of cubes."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "7396b4e8",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def all_squares_displayable(s, t):\n",
+    "    es = extended_set(s)\n",
+    "    et = extended_set(t)\n",
+    "    \n",
+    "    square_digits = ((0, 1), (0, 4), (0, 9), (1, 6), (2, 5), (3, 6), (4, 9), (6, 4), (8, 1))\n",
+    "    for (m, n) in square_digits:\n",
+    "        if not ((m in es and n in et) or (n in es and m in et)):\n",
+    "            return False\n",
+    "    \n",
+    "    return True"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9efa8055",
+   "metadata": {},
+   "source": [
+    "Then we just check all the cube pairs."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "2d11c86f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "arrangements = set()\n",
+    "for s, t in combinations(cubes(), 2):\n",
+    "    if all_squares_displayable(s, t):\n",
+    "        arrangements.add((s, t))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "8ce1fab4",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "1217"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(arrangements)"
+   ]
+  }
+ ],
+ "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
+}