Solution for the puzzle posted by 3Blue1Brown on twitter

3Blue1Brown_Puzzle.ipynb

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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solution for the puzzle posted by [3Blue1Brown on twitter](https://twitter.com/3blue1brown/status/1522749515207479302?s=20&t=BehsaJfKLV7_TBkHYwH-8Q)....."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CLOSE = 🖤\n",
      "OPEN  = 🤍\n"
     ]
    }
   ],
   "source": [
    "CLOSE = \"\\U0001F5A4\"\n",
    "OPEN = \"\\U0001F90D\"\n",
    "print(f\"CLOSE = {CLOSE}\\nOPEN  = {OPEN}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class LOCKERS():\n",
    "    def __init__(self, N, Close, Open, all_close_at_first=True):\n",
    "        self.N = N\n",
    "        self.Close = Close\n",
    "        self.Open = Open\n",
    "        self.all_close_at_first = all_close_at_first\n",
    "        self.states = []\n",
    "    \n",
    "    def __repr__(self):\n",
    "        return f\"{self.states}\"\n",
    "    \n",
    "    def initialize(self):\n",
    "        \"\"\"\n",
    "        Activate/Initialize puzzle to given state depending on flag `all_close_at_first`\n",
    "        \"\"\"\n",
    "        if self.all_close_at_first:\n",
    "            self.states = list(self.Close * self.N)\n",
    "        else:\n",
    "            self.states = list(self.Open * self.N)\n",
    "    \n",
    "    def toggle(self, state):\n",
    "        \"\"\"\n",
    "        toggle to opposite state w.r.t. given `state`\n",
    "        \"\"\"\n",
    "        if (state == self.Close):\n",
    "            return self.Open\n",
    "        if (state == self.Open):\n",
    "            return self.Close\n",
    "        \n",
    "    def solve(self):\n",
    "        \"\"\"\n",
    "        Solve the puzzle with initial state set\n",
    "        \"\"\"\n",
    "        for num in range(self.N):\n",
    "            for state_idx in range(self.N):\n",
    "                if ((state_idx + 1) % (num + 1) == 0):\n",
    "                    self.states[state_idx] = self.toggle(self.states[state_idx])\n",
    "            print(self)\n",
    "            \n",
    "    def final_ans(self):\n",
    "        \"\"\"\n",
    "        print final answer to stdout\n",
    "        \"\"\"\n",
    "        open_idxs = []\n",
    "        close_idxs = []\n",
    "        for i, o in enumerate(self.states):\n",
    "            if (o == self.Close):\n",
    "                close_idxs.append(i+1)\n",
    "            if (o == self.Open):\n",
    "                open_idxs.append(i+1)\n",
    "                \n",
    "        print(self)\n",
    "        print()\n",
    "        print(f\"OPEN  LOCKS = {open_idxs}\")\n",
    "        print()\n",
    "        print(f\"CLOSE LOCKS = {close_idxs}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['🖤', '🖤', '🖤', '🖤', '🖤', '🖤', '🖤', '🖤', '🖤', '🖤']"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lockers = LOCKERS(N = 10, Close = CLOSE, Open = OPEN, all_close_at_first=True)\n",
    "lockers.initialize()\n",
    "lockers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['🤍', '🤍', '🤍', '🤍', '🤍', '🤍', '🤍', '🤍', '🤍', '🤍']\n",
      "['🤍', '🖤', '🤍', '🖤', '🤍', '🖤', '🤍', '🖤', '🤍', '🖤']\n",
      "['🤍', '🖤', '🖤', '🖤', '🤍', '🤍', '🤍', '🖤', '🖤', '🖤']\n",
      "['🤍', '🖤', '🖤', '🤍', '🤍', '🤍', '🤍', '🤍', '🖤', '🖤']\n",
      "['🤍', '🖤', '🖤', '🤍', '🖤', '🤍', '🤍', '🤍', '🖤', '🤍']\n",
      "['🤍', '🖤', '🖤', '🤍', '🖤', '🖤', '🤍', '🤍', '🖤', '🤍']\n",
      "['🤍', '🖤', '🖤', '🤍', '🖤', '🖤', '🖤', '🤍', '🖤', '🤍']\n",
      "['🤍', '🖤', '🖤', '🤍', '🖤', '🖤', '🖤', '🖤', '🖤', '🤍']\n",
      "['🤍', '🖤', '🖤', '🤍', '🖤', '🖤', '🖤', '🖤', '🤍', '🤍']\n",
      "['🤍', '🖤', '🖤', '🤍', '🖤', '🖤', '🖤', '🖤', '🤍', '🖤']\n"
     ]
    }
   ],
   "source": [
    "lockers.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['🤍', '🖤', '🖤', '🤍', '🖤', '🖤', '🖤', '🖤', '🤍', '🖤']\n",
      "\n",
      "OPEN  LOCKS = [1, 4, 9]\n",
      "\n",
      "CLOSE LOCKS = [2, 3, 5, 6, 7, 8, 10]\n"
     ]
    }
   ],
   "source": [
    "lockers.final_ans()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['🤍', '🤍', '🤍', '🤍', '🤍', '🤍', '🤍', '🤍', '🤍', '🤍']"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lockers = LOCKERS(N = 10, Close = CLOSE, Open = OPEN, all_close_at_first=False)\n",
    "lockers.initialize()\n",
    "lockers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['🖤', '🖤', '🖤', '🖤', '🖤', '🖤', '🖤', '🖤', '🖤', '🖤']\n",
      "['🖤', '🤍', '🖤', '🤍', '🖤', '🤍', '🖤', '🤍', '🖤', '🤍']\n",
      "['🖤', '🤍', '🤍', '🤍', '🖤', '🖤', '🖤', '🤍', '🤍', '🤍']\n",
      "['🖤', '🤍', '🤍', '🖤', '🖤', '🖤', '🖤', '🖤', '🤍', '🤍']\n",
      "['🖤', '🤍', '🤍', '🖤', '🤍', '🖤', '🖤', '🖤', '🤍', '🖤']\n",
      "['🖤', '🤍', '🤍', '🖤', '🤍', '🤍', '🖤', '🖤', '🤍', '🖤']\n",
      "['🖤', '🤍', '🤍', '🖤', '🤍', '🤍', '🤍', '🖤', '🤍', '🖤']\n",
      "['🖤', '🤍', '🤍', '🖤', '🤍', '🤍', '🤍', '🤍', '🤍', '🖤']\n",
      "['🖤', '🤍', '🤍', '🖤', '🤍', '🤍', '🤍', '🤍', '🖤', '🖤']\n",
      "['🖤', '🤍', '🤍', '🖤', '🤍', '🤍', '🤍', '🤍', '🖤', '🤍']\n"
     ]
    }
   ],
   "source": [
    "lockers.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['🖤', '🤍', '🤍', '🖤', '🤍', '🤍', '🤍', '🤍', '🖤', '🤍']\n",
      "\n",
      "OPEN  LOCKS = [2, 3, 5, 6, 7, 8, 10]\n",
      "\n",
      "CLOSE LOCKS = [1, 4, 9]\n"
     ]
    }
   ],
   "source": [
    "lockers.final_ans()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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