{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Euler Problem 16\n",
    "\n",
    "$2^{15}$ = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.\n",
    "\n",
    "What is the sum of the digits of the number $2^{1000}$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Seriously? Okay, probably more difficult in C."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1366\n"
     ]
    }
   ],
   "source": [
    "s = sum(map(int, str(2**1000)))\n",
    "assert(s == 1366)\n",
    "print(s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Okay, let's do it without big ints."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def double_number_string(number_string):\n",
    "    number_string = number_string[::-1] # reverse\n",
    "    result = []\n",
    "    carriage = 0\n",
    "    for c in number_string:\n",
    "        s = carriage + int(c) + int(c)\n",
    "        carriage = s // 10\n",
    "        next_digit = s % 10\n",
    "        result.append(str(next_digit))\n",
    "    if carriage > 0:\n",
    "        result.append(str(carriage))\n",
    "    result = \"\".join(result)[::-1]\n",
    "    return result\n",
    "\n",
    "assert(double_number_string(\"132\") == \"264\")\n",
    "assert(double_number_string(\"965\") == \"1930\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1366\n"
     ]
    }
   ],
   "source": [
    "def powers_of_two(n):\n",
    "    \"\"\" Retuns nth power of two as a string. \"\"\"\n",
    "    assert(n >= 0)\n",
    "    if n == 0:\n",
    "        return \"1\"\n",
    "    s = \"2\"\n",
    "    for _ in range(n - 1):\n",
    "        s = double_number_string(s)\n",
    "    return s\n",
    "\n",
    "assert(powers_of_two(3) == \"8\")\n",
    "assert(powers_of_two(10) == \"1024\")\n",
    "\n",
    "number_string = powers_of_two(1000)\n",
    "print(sum(map(int, number_string)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we go. The conversion to integer and the sum would be easy in C."
   ]
  }
 ],
 "metadata": {
  "completion_date": "Sun, 31 Aug 2014, 20:49",
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