From 41e688ebef5be3004fa0c13196812711b9708043 Mon Sep 17 00:00:00 2001
From: Neil Smith <neil.git@njae.me.uk>
Date: Tue, 21 Feb 2017 16:48:13 +0000
Subject: [PATCH] Done puzzle 41

---
 euler41.ipynb | 175 ++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 175 insertions(+)
 create mode 100644 euler41.ipynb

diff --git a/euler41.ipynb b/euler41.ipynb
new file mode 100644
index 0000000..82f8791
--- /dev/null
+++ b/euler41.ipynb
@@ -0,0 +1,175 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "true"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "load 'primes.rb'\n",
+    "load 'array-numbers.rb'"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       ":pandigital?"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "class Integer\n",
+    "  def pandigital?\n",
+    "    self.to_digits.sort == (1..Math.log10(self).ceil).to_a\n",
+    "  end\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "Math.log10(21).ceil"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[[12, [1, 2], [1, 2]], [21, [1, 2], [1, 2]], [123, [1, 2, 3], [1, 2, 3]], [132, [1, 2, 3], [1, 2, 3]], [213, [1, 2, 3], [1, 2, 3]], [231, [1, 2, 3], [1, 2, 3]], [312, [1, 2, 3], [1, 2, 3]], [321, [1, 2, 3], [1, 2, 3]], [1234, [1, 2, 3, 4], [1, 2, 3, 4]], [1243, [1, 2, 3, 4], [1, 2, 3, 4]], [1324, [1, 2, 3, 4], [1, 2, 3, 4]], [1342, [1, 2, 3, 4], [1, 2, 3, 4]], [1423, [1, 2, 3, 4], [1, 2, 3, 4]], [1432, [1, 2, 3, 4], [1, 2, 3, 4]]]"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(1..2000).map {|i| [i, i.to_digits.sort, (1..Math.log10(i).ceil).to_a]}.select {|i, ds, ms| ds == ms}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "false"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "13.pandigital?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Divisibility rule\n",
+    "A number is divisible by 3 iff the sum of its digits is divisible by 3. Therefore, all pandigital numbers, apart from those to 4 and 7, are composite. \n",
+    "\n",
+    "Therefore, we check just the seven digit primes first."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "7652413"
+      ]
+     },
+     "execution_count": 30,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(1..7).to_a.permutation.select {|ds| ds.to_i.prime?}.map {|ds| ds.to_i}.max"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Ruby 2.4.0",
+   "language": "ruby",
+   "name": "ruby"
+  },
+  "language_info": {
+   "file_extension": ".rb",
+   "mimetype": "application/x-ruby",
+   "name": "ruby",
+   "version": "2.4.0"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
-- 
2.34.1