{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "# Powerful digit sum (Euler Problem 56)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "A googol ($10^{100}$) is a massive number: one followed by one-hundred zeros; $100^{100}$ is almost unimaginably large: one followed by two-hundred zeros. Despite their size, the sum of the digits in each number is only 1.\n",
    "\n",
    "Considering natural numbers of the form, $a^b$, where $a, b < 100$, what is the maximum digital sum?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_digit_sum(n):\n",
    "    s = 0\n",
    "    while n != 0:\n",
    "        s += (n % 10)\n",
    "        n //= 10\n",
    "    return s\n",
    "\n",
    "assert(get_digit_sum(1337) == 14)\n",
    "assert(get_digit_sum(100**100) == 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "972\n"
     ]
    }
   ],
   "source": [
    "s = max([get_digit_sum(a**b) for a in range(1, 100) for b in range(1, 100)])\n",
    "print(s)\n",
    "assert(s == 972)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "completion_date": "Mon, 24 Dec 2018, 23:33",
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  "tags": [
   "power",
   "brute force"
  ]
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