hello.ipynb

hello.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The intuition is that it's useful to solve the following equation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = 808017424794512875886459904961710757005754368000000000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[30, 6, 4, 10], [22, -2, 8, 8], [-16, -6, -5, -4], [8, 28, 10, 27]]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def exp(x):\n",
    "    res = [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]\n",
    "    for i in range(0, 4):\n",
    "        for j in range(0, 4):\n",
    "            for k in range(0, 4):\n",
    "                res[i][j] += x[i][k] * x[k][j]\n",
    "    return res\n",
    "\n",
    "A = [[1, 3, 2, 4], [3, 1, 4, 2], [2, -4, 1, -2], [4, 2, -3, 1]]\n",
    "exp(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Matrix:\n",
    "    def __init__(self, x):\n",
    "        self.A = x\n",
    "    \n",
    "    def mult(self, B):\n",
    "        res = [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]\n",
    "        for i in range(0, 4):\n",
    "            for j in range(0, 4):\n",
    "                for k in range(0, 4):\n",
    "                    res[i][j] += self.A[i][k] * B[k][j]\n",
    "        return Matrix(res)\n",
    "\n",
    "A = [\n",
    "    [1,  3,  2,  4],\n",
    "    [3,  1,  4,  2],\n",
    "    [2, -4,  1, -2],\n",
    "    [4,  2, -2,  1]\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = Matrix(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1024\n",
      "2048\n",
      "3072\n",
      "4096\n",
      "5120\n",
      "6144\n",
      "7168\n",
      "8192\n",
      "9216\n",
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      "51200\n",
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      "96256\n",
      "97280\n",
      "98304\n",
      "99328\n",
      "100352\n",
      "101376\n",
      "102400\n",
      "103424\n",
      "104448\n"
     ]
    }
   ],
   "source": [
    "from itertools import chain\n",
    "B = Matrix(A)\n",
    "is_done = False\n",
    "counter = 0\n",
    "while True:\n",
    "    B = B.mult(A)\n",
    "    new_world = list(chain.from_iterable(B.A))\n",
    "    if x in new_world:\n",
    "        print(\"Hello World!\")\n",
    "        is_done = True\n",
    "        break\n",
    "    counter += 1\n",
    "    if counter % 1024 == 0:\n",
    "        print(counter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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