{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "# Euler Problem 34\n",
    "\n",
    "145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.\n",
    "\n",
    "Find the sum of all numbers which are equal to the sum of the factorial of their digits.\n",
    "\n",
    "Note: as 1! = 1 and 2! = 2 are not sums they are not included."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The algorithm for checking if a number is curious should be efficient. The more difficult thing is to select the upper bound for the brute force. It can be seen that $9 999 999 < 9! * 7$. Hence we can select $10^7$ as our bound."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from math import factorial\n",
    "\n",
    "def is_curious(n):\n",
    "    s = sum([factorial(int(d)) for d in str(n)])\n",
    "    return n == s\n",
    "\n",
    "assert(is_curious(145) == True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "s = sum([n for n in range(3, 10**7) if is_curious(n)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "40730"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "assert(s == 40730)\n",
    "s"
   ]
  }
 ],
 "metadata": {
  "completion_date": "Mon, 12 Feb 2018, 17:57",
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   "display_name": "Python 3",
   "language": "python",
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  "tags": [
   "factorial",
   "brute force"
  ]
 },
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}