From 06eab4451b58fc623e32bdf4f426bf6104bcb6b8 Mon Sep 17 00:00:00 2001
From: filifa <filifa.breath652@8alias.com>
Date: Mon, 30 Jun 2025 22:07:49 -0400
Subject: [PATCH] add problem 93

---
 notebooks/problem0093.ipynb | 123 ++++++++++++++++++++++++++++++++++++
 1 file changed, 123 insertions(+)
 create mode 100644 notebooks/problem0093.ipynb

diff --git a/notebooks/problem0093.ipynb b/notebooks/problem0093.ipynb
new file mode 100644
index 0000000..825bab5
--- /dev/null
+++ b/notebooks/problem0093.ipynb
@@ -0,0 +1,123 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "89053792",
+   "metadata": {},
+   "source": [
+    "# [Arithmetic Expressions](https://projecteuler.net/problem=93)\n",
+    "\n",
+    "We can brute force this answer.\n",
+    "\n",
+    "There are five ways to place the parentheses in an expression with four numbers (I'm only using addition here, but obviously you could use any operators):\n",
+    "* $((a+b)+c)+d$\n",
+    "* $(a+(b+c))+d$\n",
+    "* $a+((b+c)+d)$\n",
+    "* $a+(b+(c+d))$\n",
+    "* $(a+b)+(c+d)$\n",
+    "\n",
+    "(It turns out that the number of ways to place the parentheses around $n$ numbers is $C_{n-1}$, where $C_n$ is the $n$th [Catalan number](https://en.wikipedia.org/wiki/Catalan_number).)\n",
+    "\n",
+    "If we iterate through every possible permutation of four digits, along with every possible set of three operators, and evaluate using each of the five possible groupings, we can get every number that can be formed from four digits under the problem's rules.\n",
+    "\n",
+    "Here's a function to find the longest streak of positive integers you can form from four digits."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "0d75c8ce",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from itertools import product, permutations, count\n",
+    "from operator import add, sub, mul, truediv\n",
+    "\n",
+    "def streak(digits):\n",
+    "    targets = set()\n",
+    "    for (a, b, c, d) in permutations(digits):\n",
+    "        for (op1, op2, op3) in product((add, sub, mul, truediv), repeat=3):\n",
+    "            try:\n",
+    "                targets.add(op3(op2(op1(a, b), c), d))\n",
+    "            except ZeroDivisionError:\n",
+    "                pass\n",
+    "            \n",
+    "            try:\n",
+    "                targets.add(op3(op2(a, op1(b, c)), d))\n",
+    "            except ZeroDivisionError:\n",
+    "                pass\n",
+    "            \n",
+    "            try:\n",
+    "                targets.add(op3(a, op2(op1(b, c), d)))\n",
+    "            except ZeroDivisionError:\n",
+    "                pass\n",
+    "            \n",
+    "            try:\n",
+    "                targets.add(op3(a, op2(b, op1(c, d))))\n",
+    "            except ZeroDivisionError:\n",
+    "                pass\n",
+    "            \n",
+    "            try:\n",
+    "                targets.add(op3(op1(a, b), op2(c, d)))\n",
+    "            except ZeroDivisionError:\n",
+    "                pass\n",
+    "            \n",
+    "    for n in count(1):\n",
+    "        if n not in targets:\n",
+    "            return n - 1"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7ef3f5d3",
+   "metadata": {},
+   "source": [
+    "Now we just try every combination of four digits."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "90d4d5dd",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(1, 2, 5, 8)"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "from itertools import combinations\n",
+    "\n",
+    "max(combinations(range(0, 10), 4), key=streak)"
+   ]
+  }
+ ],
+ "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
+}