From 31adaa8c6015dd5cd2d70b3b21813c40820f962e Mon Sep 17 00:00:00 2001
From: Neil Smith <neil.git@njae.me.uk>
Date: Fri, 17 Mar 2017 17:25:31 +0000
Subject: [PATCH] Done puzzle 48

---
 euler48.ipynb | 149 ++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 149 insertions(+)
 create mode 100644 euler48.ipynb

diff --git a/euler48.ipynb b/euler48.ipynb
new file mode 100644
index 0000000..0497bf6
--- /dev/null
+++ b/euler48.ipynb
@@ -0,0 +1,149 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       ":modular_exponent"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Calculate ( n ** e ) mod b\n",
+    "def modular_exponent(n, e, b)\n",
+    "  e_prime = 1\n",
+    "  c = n % b\n",
+    "  while e_prime < e\n",
+    "    c = (c * n) % b\n",
+    "    e_prime += 1\n",
+    "  end\n",
+    "  c\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "4"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "modular_exponent 4, 3, 10"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       ":self_powers"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "def self_powers(n_max, b)\n",
+    "  (1..n_max).map {|n| modular_exponent n, n, b}.sum % b\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "10405071317"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "self_powers 10, 1000000000000"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "9110846700"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "self_powers 1000, 10**10"
+   ]
+  },
+  {
+   "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