Unmask The Secret Santas.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The 41 FiveThirtyEight staff members have decided to send gifts to each other as part of a Secret Santa program. Each person is randomly assigned one of the other 40 people on the masthead to give a gift to, and they can’t give to themselves. After the Secret Santa is over, everybody naturally wants to find out who gave them their gift. So, each of them decides to ask up to 20 people who they were a Secret Santa for. If they can’t find the person who gave them the gift within 20 tries, they give up. (Twenty co-workers is a lot of co-workers to talk to, after all.) Each person asks and answers individually — they don’t tell who anyone else’s Secret Santa is. Also, nobody asks any question other than “Who were you Secret Santa for?”\n",
    "\n",
    "If each person asks questions optimally, giving themselves the best chance to unmask their Secret Santa, what is the probability that everyone finds out who their Secret Santa was? And what is this optimal strategy? (Asking randomly won’t work, because only half the people will find their Secret Santa that way on average, and there’s about a 1-in-2 trillion chance that everyone will know.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import Counter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "num_staff = 41"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "max_tries = num_staff // 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = np.arange(num_staff)\n",
    "np.random.shuffle(x)\n",
    "while np.any(x == np.arange(num_staff)):\n",
    "    np.random.shuffle(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([13,  3, 31,  8, 34, 16,  4, 33, 23, 21, 37, 14, 18, 24,  5,  9, 40,\n",
       "       22,  7, 17, 12, 38,  2, 20, 28, 10,  6,  0, 36, 39, 35,  1, 27, 25,\n",
       "       30, 11, 32, 29, 19, 26, 15])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "num_trials = 10000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def assign_secret_santas(num_staff):\n",
    "    x = np.arange(num_staff)\n",
    "    np.random.shuffle(x)\n",
    "    while np.any(x == np.arange(num_staff)):\n",
    "        np.random.shuffle(x)\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "test_assignments = np.array([assign_secret_santas(num_staff) for i in range(num_trials)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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WyutkkiTPUEb9dXK0Y6dJkpx2FltPDMDMVpnZHWb2fTO728yu7bRfa2YPdlSQvmdml8/Z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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1084aecd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "im = np.array([np.bincount(test_assignments[:, i], minlength=num_staff).tolist() for i in range(num_staff)])\n",
    "plt.imshow(im, interpolation='none', cmap=plt.cm.viridis, vmin=0, vmax=2*num_trials/float(num_staff-1))\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "assignments = np.array([assign_secret_santas(num_staff) for i in range(num_trials)])\n",
    "outcomes = np.ones(num_trials, dtype=bool)\n",
    "\n",
    "graphs = []\n",
    "\n",
    "def ask_coworker(secret_santas, my_index, coworker_index, try_number=0):\n",
    "    if try_number > max_tries:\n",
    "        return False\n",
    "    elif coworker_index == my_index:\n",
    "        return True\n",
    "    else:\n",
    "        return ask_coworker(secret_santas, my_index, secret_santas[coworker_index], try_number + 1)\n",
    "    \n",
    "def run_trial(i):\n",
    "    for coworker_index in np.arange(num_staff):\n",
    "        coworker_index = np.mod((coworker_index + np.random.randint(1, num_staff)), num_staff)\n",
    "        outcome = ask_coworker(assignments[i], coworker_index, assignments[i, coworker_index], 0)\n",
    "        if not outcome:\n",
    "            outcomes[i] = False\n",
    "            # if someone can't find their secret santa, bail on this trial\n",
    "            break\n",
    "    \n",
    "for i in range(num_trials):\n",
    "    run_trial(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#np.savez('santas_assignments.npz', assignments)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import networkx as nx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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viBWWKTmWQxlCOJq08MGbBrcl6gkVlgJg8TLaEsHYLAtHIBxNETTUEZFDyMye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\nS7KWr4eZC2lMtHKRhgz3iv2lVRaO4G1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SnmwSsMQ5Fyv0QkRa0hbBPHPO/QV4MhzilXPf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\nwAAAAA5JREFUS0REREREJEf+P8wO8VLz+MsmAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a25f290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = nx.Graph(zip(np.arange(num_staff), assignments[np.random.randint(num_trials)]))\n",
    "graphs = list(nx.connected_component_subgraphs(G))\n",
    "loop_sizes = [g.number_of_nodes() for g in graphs]\n",
    "plt.figure(figsize=(12, 4), frameon=False)\n",
    "for i, g in enumerate(graphs):\n",
    "    color = 'orange' if g.number_of_nodes() > max_tries else 'dodgerblue'\n",
    "    nx.draw_networkx(g, pos=nx.spring_layout(g, k=0.01, iterations=1000, center=(i, 0), scale=1.0/3.0), \n",
    "        node_size=200, node_color=color, font_size=8)\n",
    "plt.axis('off')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# for j in xrange(0, num_trials, 100):\n",
    "#     G = nx.Graph(zip(np.arange(num_staff), assignments[j]))\n",
    "#     graphs = list(nx.connected_component_subgraphs(G))\n",
    "#     loop_sizes = [g.number_of_nodes() for g in graphs]\n",
    "#     plt.figure(figsize=(12, 4), frameon=False)\n",
    "#     for i, g in enumerate(graphs):\n",
    "#         color = 'orange' if g.number_of_nodes() > max_tries else 'dodgerblue'\n",
    "#         nx.draw_networkx(g, pos=nx.spring_layout(g, k=0.01, iterations=1000, center=(i, 0), scale=1.0/3.0), \n",
    "#             node_size=200, node_color=color, font_size=8)\n",
    "#     plt.axis('off')\n",
    "#     plt.tight_layout()\n",
    "#     plt.savefig('santas/{:06d}.png'.format(j), dpi=75, bbox_inches='tight')\n",
    "#     plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# np.mean(outcomes[np.arange(0, num_trials, 100)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# !montage 0*png -tile 5x20 -geometry 120x40+1+1 montage.png"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}