dee_and_dum.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tweedledee and Tweedledum\n",
    "Alice stumbled on Tweedledum and Tweedledee who were grinning under a tree right by their house. Tweedledee and Tweedledum appear identical. If a brother is holding a red card, he will tell the truth, if he is holding a black card he will lie. The two brothers emerge from the house, and each makes a statement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "bro = ['Tweedledee', 'Tweedledum']\n",
    "card = ['black', 'red']\n",
    "dums = []\n",
    "dees = []\n",
    "for c in card:\n",
    "    dums = dums + [('Tweedledum', c)]\n",
    "    dees = dees + [('Tweedledee', c)]\n",
    "\n",
    "goals = []\n",
    "for dum in dums:\n",
    "    for dee in dees:\n",
    "        goals = goals + [(dum, dee)]\n",
    "        goals = goals + [(dee, dum)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "bro0Truths = []\n",
    "bro1Truths = []\n",
    "for g in goals:\n",
    "    if g[0][1] == 'red':\n",
    "        bro0Truths.append(g)\n",
    "    if g[1][1] == 'red':\n",
    "        bro1Truths.append(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def complement(listOfGoals):\n",
    "    return [g for g in goals if g not in listOfGoals]\n",
    "\n",
    "def intersect(a, b):\n",
    "    return [item for item in a if item in b]\n",
    "    \n",
    "def union(a, b):\n",
    "    return list(a) + [item for item in b if item not in a]    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "bro0Lies = complement(bro0Truths)\n",
    "bro1Lies = complement(bro1Truths)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def broForName(number, name):\n",
    "    blist = []\n",
    "    for g in goals:\n",
    "        if g[number][0] == name:\n",
    "            blist.append(g)\n",
    "    return blist\n",
    "\n",
    "def broForCard(number, card):\n",
    "    blist = []\n",
    "    for g in goals:\n",
    "        if g[number][1] == card:\n",
    "            blist.append(g)\n",
    "    return blist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 69 from Alice in PuzzleLand\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "bro0Text = \"My brother is Tweedledee and he has a black card\"\n",
    "bro1Text = \"My brother is Tweedledum and he has a red card\"\n",
    "bro0Statement = intersect(broForName(1,'Tweedledee'),broForCard(1,'black'))\n",
    "bro1Statement = intersect(broForName(0,'Tweedledum'),broForCard(0,'red'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(('Tweedledum', 'black'), ('Tweedledee', 'black')), (('Tweedledum', 'red'), ('Tweedledee', 'black'))]\n",
      "[(('Tweedledum', 'red'), ('Tweedledee', 'black')), (('Tweedledum', 'red'), ('Tweedledee', 'red'))]\n"
     ]
    }
   ],
   "source": [
    "print(bro0Statement)\n",
    "print(bro1Statement)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "bro0 = union(intersect(bro0Statement,bro0Truths),intersect(complement(bro0Statement),bro0Lies))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(('Tweedledum', 'red'), ('Tweedledee', 'black')), (('Tweedledee', 'black'), ('Tweedledum', 'black')), (('Tweedledum', 'black'), ('Tweedledee', 'red')), (('Tweedledee', 'black'), ('Tweedledum', 'red'))]\n"
     ]
    }
   ],
   "source": [
    "print(bro0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "bro1 = union(intersect(bro1Statement,bro1Truths),intersect(complement(bro1Statement),bro1Lies))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = intersect(bro0, bro1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The solution is: [(('Tweedledee', 'black'), ('Tweedledum', 'black'))]\n"
     ]
    }
   ],
   "source": [
    "print(\"The solution is: \" + str(p))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Puzzle Solver"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we define a puzzle solving function - given a statement from each brother, we use the known 'true and false' options to create a list of all possible outcomes from the statments. If the statements from both brothers result in only one possible outcome, the puzzle has a solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def goalFromStatements(b0_statement, b1_statement, output=False):\n",
    "    if (output):\n",
    "        print(\"bro 0 statement \" + str(b0_statement))\n",
    "        print(\"bro 1 statement \" + str(b1_statement))\n",
    "    b0t = intersect(b0_statement, bro0Truths) \n",
    "    if (output):\n",
    "        print('bro 0 truth: ' + str(b0t))\n",
    "    b0l = intersect(complement(b0_statement), bro0Lies)\n",
    "    if (output):\n",
    "        print('bro 0 lies: ' + str(b0l))\n",
    "    b0 = union(b0t, b0l)\n",
    "    if (output):\n",
    "        print('bro 0 possibilities: ' + str(b0))\n",
    "    b1t = intersect(b1_statement, bro1Truths) \n",
    "    if (output):\n",
    "        print('bro 1 truth: ' + str(b1t))\n",
    "    b1l = intersect(complement(b1_statement), bro1Lies)\n",
    "    if (output):\n",
    "        print('bro 1 lies: ' + str(b1l))  \n",
    "    b1 = union(b1t, b1l)\n",
    "    if (output):\n",
    "        print('bro1 possibilities: ' + str(b1))\n",
    "    hiddenGoal = intersect(b0,b1)\n",
    "    if (output):\n",
    "        print(str(hiddenGoal))\n",
    "    if (len(hiddenGoal) == 1):\n",
    "        return hiddenGoal[0]\n",
    "    else:\n",
    "        return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "bro 0 statement [(('Tweedledum', 'black'), ('Tweedledee', 'black')), (('Tweedledum', 'red'), ('Tweedledee', 'black'))]\n",
      "bro 1 statement [(('Tweedledum', 'red'), ('Tweedledee', 'black')), (('Tweedledum', 'red'), ('Tweedledee', 'red'))]\n",
      "bro 0 truth: [(('Tweedledum', 'red'), ('Tweedledee', 'black'))]\n",
      "bro 0 lies: [(('Tweedledee', 'black'), ('Tweedledum', 'black')), (('Tweedledum', 'black'), ('Tweedledee', 'red')), (('Tweedledee', 'black'), ('Tweedledum', 'red'))]\n",
      "bro 0 possibilities: [(('Tweedledum', 'red'), ('Tweedledee', 'black')), (('Tweedledee', 'black'), ('Tweedledum', 'black')), (('Tweedledum', 'black'), ('Tweedledee', 'red')), (('Tweedledee', 'black'), ('Tweedledum', 'red'))]\n",
      "bro 1 truth: [(('Tweedledum', 'red'), ('Tweedledee', 'red'))]\n",
      "bro 1 lies: [(('Tweedledum', 'black'), ('Tweedledee', 'black')), (('Tweedledee', 'black'), ('Tweedledum', 'black')), (('Tweedledee', 'red'), ('Tweedledum', 'black'))]\n",
      "bro1 possibilities: [(('Tweedledum', 'red'), ('Tweedledee', 'red')), (('Tweedledum', 'black'), ('Tweedledee', 'black')), (('Tweedledee', 'black'), ('Tweedledum', 'black')), (('Tweedledee', 'red'), ('Tweedledum', 'black'))]\n",
      "[(('Tweedledee', 'black'), ('Tweedledum', 'black'))]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(('Tweedledee', 'black'), ('Tweedledum', 'black'))"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "goalFromStatements(bro0Statement,bro1Statement,True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we define a set of statments for the brothers to use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def selfStatement(number, name, card):\n",
    "    return {'text': \"My name is \" + name + \", and I have a \" + card + \" card.\", 'list': intersect(broForName(number, name),broForCard(number,card))}\n",
    "\n",
    "def selfOrStatement(number, name, card):\n",
    "    return {'text': \"My name is \" + name + \" or I have a \" + card + \" card.\", 'list': union(broForName(number, name),broForCard(number,card))}\n",
    "\n",
    "def otherStatement(number, name, card):\n",
    "    return {'text': \"My brother's name is \" + name + \", and he has a \" + card + \" card.\", 'list': intersect(broForName(number, name),broForCard(number,card))}\n",
    "\n",
    "def otherOrStatement(number, name, card):\n",
    "    return {'text': \"My brother's name is \" + name + \" or he has a \" + card + \" card.\", 'list': union(broForName(number, name),broForCard(number,card))}\n",
    "\n",
    "def selfNameStatement(number, name):\n",
    "    return {'text': \"My name is \" + name + \".\", 'list': broForName(number, name)}\n",
    "\n",
    "def otherNameStatement(number, name):\n",
    "    return {'text': \"My brother's name is \" + name + \".\", 'list': broForName(number, name)}\n",
    "\n",
    "def selfCardStatement(number, card):\n",
    "    return {'text': \"I have a \" + card + \" card.\", 'list': broForCard(number, card)}\n",
    "\n",
    "def otherCardStatement(number, card):\n",
    "    return {'text': \"My brother has a \" + card + \" card.\", 'list': broForCard(number, card)}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'text': 'My name is Tweedledee, and I have a red card.',\n",
       " 'list': [(('Tweedledee', 'red'), ('Tweedledum', 'black')),\n",
       "  (('Tweedledee', 'red'), ('Tweedledum', 'red'))]}"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "selfStatement(0,'Tweedledee','red')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'text': 'My name is Tweedledee, and I have a black card.',\n",
       " 'list': [(('Tweedledee', 'black'), ('Tweedledum', 'black')),\n",
       "  (('Tweedledee', 'black'), ('Tweedledum', 'red'))]}"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "selfStatement(0,'Tweedledee','black')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'text': \"My brother's name is Tweedledee, and he has a red card.\",\n",
       " 'list': [(('Tweedledum', 'black'), ('Tweedledee', 'red')),\n",
       "  (('Tweedledum', 'red'), ('Tweedledee', 'red'))]}"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "otherStatement(1,'Tweedledee','red')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bro0Statements = []\n",
    "for b in bro:\n",
    "    for c in card:\n",
    "        bro0Statements.append(selfStatement(0,b,c))\n",
    "        bro0Statements.append(otherStatement(1,b,c))\n",
    "        bro0Statements.append(selfOrStatement(0,b,c))\n",
    "        bro0Statements.append(otherOrStatement(1,b,c))\n",
    "for b in bro:\n",
    "    bro0Statements.append(selfNameStatement(0,b))\n",
    "    bro0Statements.append(otherNameStatement(1,b))\n",
    "for c in card:\n",
    "    bro0Statements.append(selfCardStatement(0,c))\n",
    "    bro0Statements.append(otherCardStatement(1,c))\n",
    "len(bro0Statements)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bro1Statements = []\n",
    "for b in bro:\n",
    "    for c in card:\n",
    "        bro1Statements.append(selfStatement(1,b,c))\n",
    "        bro1Statements.append(otherStatement(0,b,c))\n",
    "        bro1Statements.append(selfOrStatement(1,b,c))\n",
    "        bro1Statements.append(otherOrStatement(0,b,c))\n",
    "for b in bro:\n",
    "    bro1Statements.append(selfNameStatement(1,b))\n",
    "    bro1Statements.append(otherNameStatement(0,b))\n",
    "for c in card:\n",
    "    bro1Statements.append(selfCardStatement(1,c))\n",
    "    bro1Statements.append(otherCardStatement(0,c))\n",
    "len(bro1Statements)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally we iterate over all combinations of the statements from the two brothers to find the ones that generate a solvable puzzle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The first brother says: My name is Tweedledee, and I have a black card.\n",
      "The second brother says: My brother's name is Tweedledee, and he has a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee, and I have a black card.\n",
      "The second brother says: My name is Tweedledee or I have a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee, and I have a black card.\n",
      "The second brother says: My brother's name is Tweedledee or he has a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee, and I have a black card.\n",
      "The second brother says: My brother's name is Tweedledee, and he has a red card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee, and I have a black card.\n",
      "The second brother says: My name is Tweedledee or I have a red card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee, and I have a black card.\n",
      "The second brother says: My brother's name is Tweedledee or he has a red card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee, and I have a black card.\n",
      "The second brother says: My name is Tweedledum, and I have a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee, and I have a black card.\n",
      "The second brother says: My brother's name is Tweedledum, and he has a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee, and I have a black card.\n",
      "The second brother says: My brother's name is Tweedledum or he has a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee, and I have a black card.\n",
      "The second brother says: My name is Tweedledum, and I have a red card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee, and I have a black card.\n",
      "The second brother says: My brother's name is Tweedledum, and he has a red card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee, and I have a black card.\n",
      "The second brother says: My brother's name is Tweedledum or he has a red card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee, and I have a black card.\n",
      "The second brother says: My name is Tweedledee.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee, and I have a black card.\n",
      "The second brother says: My brother's name is Tweedledee.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee, and I have a black card.\n",
      "The second brother says: My name is Tweedledum.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee, and I have a black card.\n",
      "The second brother says: My brother's name is Tweedledum.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee, and I have a black card.\n",
      "The second brother says: My brother has a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee, and I have a black card.\n",
      "The second brother says: My brother has a red card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee, and he has a black card.\n",
      "The second brother says: My name is Tweedledee, and I have a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee, and he has a black card.\n",
      "The second brother says: My name is Tweedledee or I have a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee, and he has a black card.\n",
      "The second brother says: My brother's name is Tweedledee or he has a red card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee, and he has a black card.\n",
      "The second brother says: My name is Tweedledum, and I have a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee, and he has a black card.\n",
      "The second brother says: My name is Tweedledum or I have a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee, and he has a black card.\n",
      "The second brother says: My brother's name is Tweedledum, and he has a red card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee, and he has a black card.\n",
      "The second brother says: My brother has a red card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee or I have a black card.\n",
      "The second brother says: My name is Tweedledee, and I have a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee or I have a black card.\n",
      "The second brother says: My brother's name is Tweedledee, and he has a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee or I have a black card.\n",
      "The second brother says: My brother's name is Tweedledee or he has a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee or I have a black card.\n",
      "The second brother says: My name is Tweedledee, and I have a red card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee or I have a black card.\n",
      "The second brother says: My brother's name is Tweedledee, and he has a red card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee or I have a black card.\n",
      "The second brother says: My brother's name is Tweedledee or he has a red card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee or I have a black card.\n",
      "The second brother says: My brother's name is Tweedledum, and he has a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee or I have a black card.\n",
      "The second brother says: My name is Tweedledum or I have a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee or I have a black card.\n",
      "The second brother says: My brother's name is Tweedledum or he has a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee or I have a black card.\n",
      "The second brother says: My brother's name is Tweedledum, and he has a red card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee or I have a black card.\n",
      "The second brother says: My name is Tweedledum or I have a red card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee or I have a black card.\n",
      "The second brother says: My brother's name is Tweedledum or he has a red card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee or I have a black card.\n",
      "The second brother says: My name is Tweedledee.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee or I have a black card.\n",
      "The second brother says: My brother's name is Tweedledee.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee or I have a black card.\n",
      "The second brother says: My name is Tweedledum.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee or I have a black card.\n",
      "The second brother says: My brother's name is Tweedledum.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee or I have a black card.\n",
      "The second brother says: My brother has a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee or I have a black card.\n",
      "The second brother says: My brother has a red card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee or he has a black card.\n",
      "The second brother says: My name is Tweedledee, and I have a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee or he has a black card.\n",
      "The second brother says: My name is Tweedledee or I have a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee or he has a black card.\n",
      "The second brother says: My brother's name is Tweedledee, and he has a red card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee or he has a black card.\n",
      "The second brother says: My name is Tweedledum, and I have a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee or he has a black card.\n",
      "The second brother says: My name is Tweedledum or I have a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee or he has a black card.\n",
      "The second brother says: My brother's name is Tweedledum or he has a red card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee or he has a black card.\n",
      "The second brother says: My brother has a red card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee, and I have a red card.\n",
      "The second brother says: My name is Tweedledee or I have a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee, and I have a red card.\n",
      "The second brother says: My name is Tweedledum, and I have a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee, and he has a red card.\n",
      "The second brother says: My name is Tweedledee, and I have a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee, and he has a red card.\n",
      "The second brother says: My name is Tweedledee or I have a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee, and he has a red card.\n",
      "The second brother says: My brother's name is Tweedledee or he has a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee, and he has a red card.\n",
      "The second brother says: My name is Tweedledum, and I have a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee, and he has a red card.\n",
      "The second brother says: My brother's name is Tweedledum, and he has a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee, and he has a red card.\n",
      "The second brother says: My name is Tweedledum or I have a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee, and he has a red card.\n",
      "The second brother says: My brother has a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee or I have a red card.\n",
      "The second brother says: My name is Tweedledee, and I have a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee or I have a red card.\n",
      "The second brother says: My name is Tweedledum or I have a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee or he has a red card.\n",
      "The second brother says: My name is Tweedledee, and I have a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee or he has a red card.\n",
      "The second brother says: My brother's name is Tweedledee, and he has a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee or he has a red card.\n",
      "The second brother says: My name is Tweedledee or I have a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee or he has a red card.\n",
      "The second brother says: My name is Tweedledum, and I have a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee or he has a red card.\n",
      "The second brother says: My name is Tweedledum or I have a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee or he has a red card.\n",
      "The second brother says: My brother's name is Tweedledum or he has a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee or he has a red card.\n",
      "The second brother says: My brother has a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum, and I have a black card.\n",
      "The second brother says: My name is Tweedledee, and I have a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum, and I have a black card.\n",
      "The second brother says: My brother's name is Tweedledee, and he has a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum, and I have a black card.\n",
      "The second brother says: My brother's name is Tweedledee or he has a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum, and I have a black card.\n",
      "The second brother says: My name is Tweedledee, and I have a red card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum, and I have a black card.\n",
      "The second brother says: My brother's name is Tweedledee, and he has a red card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum, and I have a black card.\n",
      "The second brother says: My brother's name is Tweedledee or he has a red card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum, and I have a black card.\n",
      "The second brother says: My brother's name is Tweedledum, and he has a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum, and I have a black card.\n",
      "The second brother says: My name is Tweedledum or I have a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum, and I have a black card.\n",
      "The second brother says: My brother's name is Tweedledum or he has a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum, and I have a black card.\n",
      "The second brother says: My brother's name is Tweedledum, and he has a red card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum, and I have a black card.\n",
      "The second brother says: My name is Tweedledum or I have a red card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum, and I have a black card.\n",
      "The second brother says: My brother's name is Tweedledum or he has a red card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum, and I have a black card.\n",
      "The second brother says: My name is Tweedledee.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum, and I have a black card.\n",
      "The second brother says: My brother's name is Tweedledee.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum, and I have a black card.\n",
      "The second brother says: My name is Tweedledum.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum, and I have a black card.\n",
      "The second brother says: My brother's name is Tweedledum.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum, and I have a black card.\n",
      "The second brother says: My brother has a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum, and I have a black card.\n",
      "The second brother says: My brother has a red card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum, and he has a black card.\n",
      "The second brother says: My name is Tweedledee, and I have a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum, and he has a black card.\n",
      "The second brother says: My name is Tweedledee or I have a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum, and he has a black card.\n",
      "The second brother says: My brother's name is Tweedledee, and he has a red card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum, and he has a black card.\n",
      "The second brother says: My name is Tweedledum, and I have a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum, and he has a black card.\n",
      "The second brother says: My name is Tweedledum or I have a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum, and he has a black card.\n",
      "The second brother says: My brother's name is Tweedledum or he has a red card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum, and he has a black card.\n",
      "The second brother says: My brother has a red card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum or I have a black card.\n",
      "The second brother says: My brother's name is Tweedledee, and he has a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum or I have a black card.\n",
      "The second brother says: My name is Tweedledee or I have a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum or I have a black card.\n",
      "The second brother says: My brother's name is Tweedledee or he has a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum or I have a black card.\n",
      "The second brother says: My brother's name is Tweedledee, and he has a red card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum or I have a black card.\n",
      "The second brother says: My name is Tweedledee or I have a red card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum or I have a black card.\n",
      "The second brother says: My brother's name is Tweedledee or he has a red card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum or I have a black card.\n",
      "The second brother says: My name is Tweedledum, and I have a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum or I have a black card.\n",
      "The second brother says: My brother's name is Tweedledum, and he has a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum or I have a black card.\n",
      "The second brother says: My brother's name is Tweedledum or he has a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum or I have a black card.\n",
      "The second brother says: My name is Tweedledum, and I have a red card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum or I have a black card.\n",
      "The second brother says: My brother's name is Tweedledum, and he has a red card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum or I have a black card.\n",
      "The second brother says: My brother's name is Tweedledum or he has a red card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum or I have a black card.\n",
      "The second brother says: My name is Tweedledee.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum or I have a black card.\n",
      "The second brother says: My brother's name is Tweedledee.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum or I have a black card.\n",
      "The second brother says: My name is Tweedledum.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum or I have a black card.\n",
      "The second brother says: My brother's name is Tweedledum.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum or I have a black card.\n",
      "The second brother says: My brother has a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum or I have a black card.\n",
      "The second brother says: My brother has a red card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum or he has a black card.\n",
      "The second brother says: My name is Tweedledee, and I have a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum or he has a black card.\n",
      "The second brother says: My name is Tweedledee or I have a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum or he has a black card.\n",
      "The second brother says: My brother's name is Tweedledee or he has a red card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum or he has a black card.\n",
      "The second brother says: My name is Tweedledum, and I have a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum or he has a black card.\n",
      "The second brother says: My name is Tweedledum or I have a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum or he has a black card.\n",
      "The second brother says: My brother's name is Tweedledum, and he has a red card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum or he has a black card.\n",
      "The second brother says: My brother has a red card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum, and I have a red card.\n",
      "The second brother says: My name is Tweedledee, and I have a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum, and I have a red card.\n",
      "The second brother says: My name is Tweedledum or I have a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum, and he has a red card.\n",
      "The second brother says: My name is Tweedledee, and I have a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum, and he has a red card.\n",
      "The second brother says: My brother's name is Tweedledee, and he has a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum, and he has a red card.\n",
      "The second brother says: My name is Tweedledee or I have a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum, and he has a red card.\n",
      "The second brother says: My name is Tweedledum, and I have a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum, and he has a red card.\n",
      "The second brother says: My name is Tweedledum or I have a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum, and he has a red card.\n",
      "The second brother says: My brother's name is Tweedledum or he has a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum, and he has a red card.\n",
      "The second brother says: My brother has a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum or I have a red card.\n",
      "The second brother says: My name is Tweedledee or I have a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum or I have a red card.\n",
      "The second brother says: My name is Tweedledum, and I have a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum or he has a red card.\n",
      "The second brother says: My name is Tweedledee, and I have a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum or he has a red card.\n",
      "The second brother says: My name is Tweedledee or I have a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum or he has a red card.\n",
      "The second brother says: My brother's name is Tweedledee or he has a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum or he has a red card.\n",
      "The second brother says: My name is Tweedledum, and I have a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum or he has a red card.\n",
      "The second brother says: My brother's name is Tweedledum, and he has a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum or he has a red card.\n",
      "The second brother says: My name is Tweedledum or I have a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum or he has a red card.\n",
      "The second brother says: My brother has a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee.\n",
      "The second brother says: My name is Tweedledee, and I have a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee.\n",
      "The second brother says: My name is Tweedledee or I have a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee.\n",
      "The second brother says: My name is Tweedledum, and I have a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledee.\n",
      "The second brother says: My name is Tweedledum or I have a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee.\n",
      "The second brother says: My name is Tweedledee, and I have a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee.\n",
      "The second brother says: My name is Tweedledee or I have a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee.\n",
      "The second brother says: My name is Tweedledum, and I have a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledee.\n",
      "The second brother says: My name is Tweedledum or I have a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum.\n",
      "The second brother says: My name is Tweedledee, and I have a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum.\n",
      "The second brother says: My name is Tweedledee or I have a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum.\n",
      "The second brother says: My name is Tweedledum, and I have a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My name is Tweedledum.\n",
      "The second brother says: My name is Tweedledum or I have a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum.\n",
      "The second brother says: My name is Tweedledee, and I have a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum.\n",
      "The second brother says: My name is Tweedledee or I have a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum.\n",
      "The second brother says: My name is Tweedledum, and I have a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother's name is Tweedledum.\n",
      "The second brother says: My name is Tweedledum or I have a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother has a black card.\n",
      "The second brother says: My name is Tweedledee, and I have a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother has a black card.\n",
      "The second brother says: My name is Tweedledee or I have a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother has a black card.\n",
      "The second brother says: My brother's name is Tweedledee, and he has a red card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother has a black card.\n",
      "The second brother says: My brother's name is Tweedledee or he has a red card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother has a black card.\n",
      "The second brother says: My name is Tweedledum, and I have a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother has a black card.\n",
      "The second brother says: My name is Tweedledum or I have a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother has a black card.\n",
      "The second brother says: My brother's name is Tweedledum, and he has a red card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother has a black card.\n",
      "The second brother says: My brother's name is Tweedledum or he has a red card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother has a red card.\n",
      "The second brother says: My name is Tweedledee, and I have a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother has a red card.\n",
      "The second brother says: My brother's name is Tweedledee, and he has a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother has a red card.\n",
      "The second brother says: My name is Tweedledee or I have a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother has a red card.\n",
      "The second brother says: My brother's name is Tweedledee or he has a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother has a red card.\n",
      "The second brother says: My name is Tweedledum, and I have a black card.\n",
      "solution: (('Tweedledum', 'black'), ('Tweedledee', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother has a red card.\n",
      "The second brother says: My brother's name is Tweedledum, and he has a black card.\n",
      "solution: (('Tweedledee', 'black'), ('Tweedledum', 'black'))\n",
      "-----------------\n",
      "The first brother says: My brother has a red card.\n",
      "The second brother says: My name is Tweedledum or I have a black card.\n",
      "solution: (('Tweedledee', 'red'), ('Tweedledum', 'red'))\n",
      "-----------------\n",
      "The first brother says: My brother has a red card.\n",
      "The second brother says: My brother's name is Tweedledum or he has a black card.\n",
      "solution: (('Tweedledum', 'red'), ('Tweedledee', 'red'))\n",
      "-----------------\n",
      "found 168 puzzles\n",
      "distribution: {'bro0_red': 84, 'bro0_black': 84, 'bro1_red': 84, 'bro1_black': 84}\n",
      "distribution: {'both_red': 42, 'both_black': 42, 'one_each': 84}\n"
     ]
    }
   ],
   "source": [
    "count = 0\n",
    "bro_count = {'bro0_red':0, 'bro0_black':0, 'bro1_red':0, 'bro1_black':0}\n",
    "combo_count = {'both_red':0, 'both_black':0, 'one_each':0}\n",
    "for s in bro0Statements:\n",
    "    for t in bro1Statements:\n",
    "        p = goalFromStatements(s['list'],t['list'])\n",
    "        if (p != None):\n",
    "            count = count + 1\n",
    "            print('The first brother says: ' + s['text'])\n",
    "            print('The second brother says: ' + t['text'])\n",
    "            print(\"solution: \" + str(p))\n",
    "            if (p[0][1] == 'red'):\n",
    "                bro_count['bro0_red'] = bro_count['bro0_red'] +1\n",
    "            else: \n",
    "                bro_count['bro0_black'] = bro_count['bro0_black'] +1\n",
    "            if (p[1][1] == 'red'):\n",
    "                bro_count['bro1_red'] = bro_count['bro1_red'] +1\n",
    "            else:\n",
    "                bro_count['bro1_black'] = bro_count['bro1_black'] +1\n",
    "            if (p[0][1] == 'red' and p[1][1] == 'red'):\n",
    "                combo_count['both_red'] = combo_count['both_red'] +1\n",
    "            elif (p[0][1] == 'black' and p[1][1] == 'black'):\n",
    "                combo_count['both_black'] = combo_count['both_black'] +1\n",
    "            else:\n",
    "                combo_count['one_each'] = combo_count['one_each'] +1 \n",
    "            #goalFromStatements(s['list'],t['list'],True)\n",
    "            print(\"-----------------\")\n",
    "print(\"found \" + str(count) + \" puzzles\")\n",
    "print(\"distribution: \" + str(bro_count))\n",
    "print(\"distribution: \" + str(combo_count))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Out of 24^2 = 576 possible puzzles, only 168 combinations lead to actual puzzles. There are really two equivilant ways to state the same puzzle (for any puzzle, switching the brothers creates a different but equivalent puzzle), so ultimately there are really only 84 truly distinct puzzles from these lists of statements."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The distribution of the solutions is uniform - it is just as likely for a brother to have a red card as a black card."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline \n",
    "\n",
    "height = []\n",
    "for b in bro_count:\n",
    "    height.append(bro_count[b])\n",
    "x_axis = np.arange(len(bro_count))    \n",
    "plt.barh(x_axis, height)\n",
    "plt.yticks(x_axis, bro_count)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZ0AAAD8CAYAAACsAHnpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4wLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvqOYd8AAAD/tJREFUeJzt3H2wXHV9x/H3x0RjEmwEwzARtNeHDIjyJCmCTyNCLRqrtcr4NA46jqjDgJR2OjjM0LEOmlKnoFOVRqrYymAbxGpxRKnGh0EBbwgkwRC0JQXjA1olqIwK4ds/9lxZL0nuvcnN76zJ+zWzk7O/PQ+f3T3JJ+ec3U1VIUlSC4/oO4Akad9h6UiSmrF0JEnNWDqSpGYsHUlSM5aOJKkZS0eS1IylI0lqxtKRJDUzt+8Ao2bx4sU1NjbWdwxJ+r2yZs2an1TVgVPNZ+lMMjY2xvj4eN8xJOn3SpL/nc58nl6TJDVj6UiSmrF0JEnNWDqSpGYsHUlSM5aOJKkZS0eS1IylI0lqxi+HTrJ+y1bGzv1c3zEkqanNK5Y32Y5HOpKkZiwdSVIzlo4kqRlLR5LUjKUjSWrG0pEkNWPpSJKasXQkSc1YOpKkZiwdSVIzlo4kqRlLR5LUjKUjSWrG0pEkNWPpSJKasXQkSc1YOpKkZiwdSVIzlo4kqRlLR5LUjKUjSWrG0pEkNWPpSJKasXQkSc1YOpKkZvbq0kmyOcnivnNIkgb26tKRJI2W3SqdJOck2dDdzk4ylmRjko8kuTXJF5PM7+Z9SpJrkqxJ8vUkh+1kvQcm+VSSb3W353TjxyX5ZpK1Sb6R5NBufE6S93U51iU5c2h1Zya5Kcn6HW0zyelJxpOMb7tv6+68JJKkndjl0klyLPAm4FnA8cBbgP2BpcAHq+rpwD3AK7tFVgJnVtWxwF8BH9rJ6t8PXFRVf9Qtf2k3fhvwvKo6BjgfeE83fjowBhxdVUcClw+t6ydV9Uzgw912H6aqVlbVsqpaNmfBomm+ApKkmZq7G8s+F/h0Vf0SIMlVwPOAO6rq5m6eNcBYkv2AZwOrkkwsP28n6z4ZOHxo3j/o1rEI+HiSpUABjxya/5KqegCgqn46tK6rhrL8+a48UUnS7Nid0tmRXw9NbwPmMziiuqeqjp7mOh4BHF9VvxoeTPKPwOqqekWSMeArM8izjT3zfCVJ07Q713S+DvxZkgVJFgKv6MYepqruBe5IcipABo7aybq/CPz2ukySibJaBGzppt84NP+1wFuTzO3mP2DmT0eStKftculU1U3AZcCNwA0Mrrv8bCeLvB54c5JbgFuBl+9k3rOAZd2HAr4NvK0bvxB4b5K1/O5Ry6XAncC6bv2vm/kzkiTtaamqvjOMlHlLltaS0y7uO4YkNbV5xfLdWj7JmqpaNtV8fk9HktRMrxfWk5wHnDppeFVVXdBHHknSntVr6XTlYsFI0j7C02uSpGYsHUlSM5aOJKkZS0eS1IylI0lqxtKRJDVj6UiSmrF0JEnNWDqSpGYsHUlSM5aOJKkZS0eS1IylI0lqxtKRJDVj6UiSmrF0JEnNWDqSpGYsHUlSM5aOJKmZuX0HGDVHHLyI8RXL+44hSXslj3QkSc1YOpKkZiwdSVIzlo4kqRlLR5LUjKUjSWrG0pEkNWPpSJKasXQkSc1YOpKkZiwdSVIzlo4kqRlLR5LUjL8yPcn6LVsZO/dzfcfQPmqzv3CuvZxHOpKkZiwdSVIzlo4kqRlLR5LUjKUjSWrG0pEkNWPpSJKasXQkSc1YOpKkZiwdSVIzlo4kqRlLR5LUjKUjSWrG0pEkNWPpSJKasXQkSc1YOpKkZiwdSVIzlo4kqRlLR5LUjKUjSWrG0pEkNWPpSJKasXQkSc1MWTpJxpJsmO4Kk5ydZMHQ/V/MYNnLkrxqO+MvSHL1dNczadnNSRbvyrKSpNm1J450zgYWTDmXJGmfM93SmZvk8iQbk1yZZEGSk5KsTbI+yUeTzEtyFvB4YHWS1RMLJ7kgyS1Jrk9y0BTbOjnJeJLbk7x08oNJjkvyzW7b30hyaDc+J8n7kmxIsi7JmZOWm5/k80neMs3nLEmaZdMtnUOBD1XV04B7gXOAy4BXV9URwFzg7VX1AeD7wIlVdWK37ELg+qo6CvgaMNU/+mPAccBy4JIkj570+G3A86rqGOB84D3d+OndskdX1ZHA5UPL7Af8J3BFVX1k8gaTnN4V3fi2+7ZOEU+StKumWzp3VdV13fQngJOAO6rq9m7s48Dzd7Dsb4CJ6zFrGBTDzvx7VT1YVd8B/gc4bNLji4BV3XWmi4Cnd+MnA/9UVQ8AVNVPh5b5DPCxqvqX7W2wqlZW1bKqWjZnwaIp4kmSdtV0S6cm3b9nBtu4v6omlt/G4KhoJtuafP/dwOqqegbwp8DkI6HtuQ44JUmmMa8kaQ+Zbuk8MckJ3fTrgHFgLMlTu7E3AF/tpn8OPGY3Mp2a5BFJngI8Gdg06fFFwJZu+o1D49cCb00yFyDJAUOPnQ/8DPjgbuSSJO2m6ZbOJuCMJBuB/Rmc1noTg9Nc64EHgUu6eVcC1wx/kGCG7gRuBD4PvK2qfjXp8QuB9yZZy+8eNV3aLbsuyS0MynHYO4D5SS7cxVySpN2Uh858CWDekqW15LSL+46hfdTmFcv7jiDtkiRrqmrZVPP5iwSSpGamuqi/RyQ5Dzh10vCqqrqgjzySpDZ6KZ2uXCwYSdrHeHpNktSMpSNJasbSkSQ1Y+lIkpqxdCRJzVg6kqRmLB1JUjOWjiSpGUtHktSMpSNJasbSkSQ1Y+lIkpqxdCRJzVg6kqRmLB1JUjOWjiSpGUtHktSMpSNJasbSkSQ1M7fvAKPmiIMXMb5ied8xJGmv5JGOJKkZS0eS1IylI0lqxtKRJDVj6UiSmrF0JEnNWDqSpGYsHUlSM5aOJKkZS0eS1IylI0lqxtKRJDVj6UiSmvFXpidZv2UrY+d+ru8Y2kdt9hfOtZfzSEeS1IylI0lqxtKRJDVj6UiSmrF0JEnNWDqSpGYsHUlSM5aOJKkZS0eS1IylI0lqxtKRJDVj6UiSmrF0JEnNWDqSpGYsHUlSM5aOJKkZS0eS1IylI0lqxtKRJDVj6UiSmrF0JEnNWDqSpGYsHUlSM5aOJKkZS0eS1MyslU6SsSQbZjD/2UkWDN3/xWxl2ck2v5Jk2Z7ejiRp+/o80jkbWDDlXFNIMncWskiSGpjt0pmb5PIkG5NcmWRBkpOSrE2yPslHk8xLchbweGB1ktUTCye5IMktSa5PctCONpLksiSXJLkBuDDJwm7dN3bbenk33/wkn+zyfBqYP8vPV5I0A7NdOocCH6qqpwH3AucAlwGvrqojgLnA26vqA8D3gROr6sRu2YXA9VV1FPA14C1TbOsQ4NlVdQ5wHvDlqjoOOBH4+yQLgbcD93V5/gY4dnsrSnJ6kvEk49vu27qrz12SNIXZLp27quq6bvoTwEnAHVV1ezf2ceD5O1j2N8DV3fQaYGyKba2qqm3d9IuAc5PcDHwFeDTwxG5bnwCoqnXAuu2tqKpWVtWyqlo2Z8GiKTYrSdpVs309pCbdvwd43DSXvb+qJpbfxtTZfjk0HeCVVbVpeIYk09y0JKmF2T7SeWKSE7rp1wHjwFiSp3ZjbwC+2k3/HHjMLG33C8CZ6VomyTHd+Ne6HCR5BnDkLG1PkrQLZrt0NgFnJNkI7A9cBLwJWJVkPfAgcEk370rgmuEPEuyGdwOPBNYlubW7D/BhYL8uz98yOG0nSepJHjqjJYB5S5bWktMu7juG9lGbVyzvO4K0S5KsqaopvwfpLxJIkpoZ6S9WJjkPOHXS8KqquqCPPJKk3TPSpdOViwUjSXsJT69JkpqxdCRJzVg6kqRmLB1JUjOWjiSpGUtHktSMpSNJasbSkSQ1Y+lIkpqxdCRJzVg6kqRmLB1JUjOWjiSpGUtHktSMpSNJasbSkSQ1Y+lIkpqxdCRJzVg6kqRm5vYdYNQccfAixlcs7zuGJO2VPNKRJDVj6UiSmrF0JEnNWDqSpGYsHUlSM5aOJKkZS0eS1IylI0lqxtKRJDWTquo7w0hJ8nNgU985tmMx8JO+Q2yHuWbGXDNjrpnpM9cfVtWBU83kz+A83KaqWtZ3iMmSjJtr+sw1M+aaGXPtOk+vSZKasXQkSc1YOg+3su8AO2CumTHXzJhrZsy1i/wggSSpGY90JEnNWDpDkpySZFOS7yY5t8ccH01yd5INQ2MHJLk2yXe6P/fvIdcTkqxO8u0ktyZ5xyhkS/LoJDcmuaXL9a5u/ElJbujez39L8qiWuboMc5KsTXL1CGXanGR9kpuTjHdjo7B/PTbJlUluS7IxyQl950pyaPc6TdzuTXJ237m6bH/R7e8bklzR/T3off+aiqXTSTIH+CDwYuBw4LVJDu8pzmXAKZPGzgW+VFVLgS9191t7APjLqjocOB44o3uN+s72a+CFVXUUcDRwSpLjgb8DLqqqpwI/A97cOBfAO4CNQ/dHIRPAiVV19NDHa/t+DwHeD1xTVYcBRzF43XrNVVWbutfpaOBY4D7g033nSnIwcBawrKqeAcwBXsPo7F87VlXeBte1TgC+MHT/ncA7e8wzBmwYur8JWNJNL2HwfaK+X7PPAH88StmABcBNwLMYfElu7vbe30ZZDmHwD9ILgauB9J2p2+5mYPGksV7fQ2ARcAfddeZRyTUpy4uA60YhF3AwcBdwAIPvW14N/Mko7F9T3TzSecjEmzjhe93YqDioqn7QTf8QOKjPMEnGgGOAGxiBbN1prJuBu4Frgf8G7qmqB7pZ+ng/Lwb+Gniwu/+4EcgEUMAXk6xJcno31vd7+CTgx8DHutORlyZZOAK5hr0GuKKb7jVXVW0B3gfcCfwA2AqsYTT2r52ydH4P1eC/Mb197DDJfsCngLOr6t7hx/rKVlXbanAK5BDgOOCw1hmGJXkpcHdVrekzxw48t6qeyeBU8hlJnj/8YE/v4VzgmcCHq+oY4JdMOmXV537fXRt5GbBq8mN95OquIb2cQVk/HljIw0/JjyRL5yFbgCcM3T+kGxsVP0qyBKD78+4+QiR5JIPCubyqrhqlbABVdQ+wmsGphccmmfipp9bv53OAlyXZDHySwSm29/ecCfjt/5KpqrsZXJ84jv7fw+8B36uqG7r7VzIoob5zTXgxcFNV/ai733euk4E7qurHVXU/cBWDfa73/Wsqls5DvgUs7T798SgGh9Kf7TnTsM8Cp3XTpzG4ntJUkgD/DGysqn8YlWxJDkzy2G56PoPrTBsZlM+r+shVVe+sqkOqaozBvvTlqnp9n5kAkixM8piJaQbXKTbQ83tYVT8E7kpyaDd0EvDtvnMNeS0PnVqD/nPdCRyfZEH393Li9ep1/5qWvi8qjdINeAlwO4PrAef1mOMKBudp72fwP8A3M7ge8CXgO8B/AQf0kOu5DE4jrANu7m4v6TsbcCSwtsu1ATi/G38ycCPwXQanReb19H6+ALh6FDJ127+lu906sZ/3/R52GY4Gxrv38T+A/Uck10Lg/4BFQ2OjkOtdwG3dPv+vwLy+96/p3PxFAklSM55ekyQ1Y+lIkpqxdCRJzVg6kqRmLB1JUjOWjiSpGUtHktSMpSNJaub/AYoGB74PQw/xAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "height = []\n",
    "for b in combo_count:\n",
    "    height.append(combo_count[b])\n",
    "x_axis = np.arange(len(combo_count))    \n",
    "plt.barh(x_axis, height)\n",
    "plt.yticks(x_axis, combo_count)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}