34-Solution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Birthday Holidays\n",
    "\n",
    "- Labor laws in Erewhon require factory owners to give every worker a holiday whenever **any one** of them has a birthday and to hire without discrimination on grounds of birthdays\n",
    "- Except for these holidays, they work a 365-day year\n",
    "- The owners want to maximize the expected total number of man-days worked worked per year in a factory\n",
    "- *How many workers do factories have in Erewhon?*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_____\n",
    "\n",
    "- **Note**: $\\text{Man Days} = (\\text{# of men working})\\cdot(\\text{days the factory is open})$\n",
    "\n",
    "- If any single employee has a birthday, the whole factory is shut"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- So, if the factory **has one employee**, the factory will only be closed on the one employee's birthday so the number of man days is equal to $(1)\\cdot(364) = 364$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- If the factory has 2 employees, there are 2 possible scenarios\n",
    "    - They have the same birthday\n",
    "        - Probability = (1/365); Man Days = $(2)\\cdot(364) = 728$\n",
    "    - That have different birthdays\n",
    "        - Probability = (364/365); Man Days = $(2)\\cdot(363) = 726$\n",
    "    - Therefore, the expected number of man days is equal to $(1/365)\\cdot(728) + (364/365)\\cdot(726) \\approx 726$\n",
    "    \n",
    "- We might start to think *\"since the number of workers cranks up the expected man days, why not just hire a ton of guys!?*\n",
    "    - The answer is that as we increase the number of workers, we increase the number of distinct birthdays and hence the number of days the factory must be closed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Let's think about the probability of the factory being open on any given day\n",
    "\n",
    "$$\n",
    "P(\\text{Factory is open}) = P(\\text{No one's birthday today}) = \\left (\\frac{364}{365} \\right )^{n}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Therefore, the expected number of man days worked in a year is equal to:\n",
    "\n",
    "$$\n",
    "\\text{Expected Man Days} = n\\cdot365\\cdot(364/365)^{n}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Let's plot this as a function of $n$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = 10, 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "array_n = np.arange(1, 1000)\n",
    "array_expected_man_days = array_n*365*((364/365)**array_n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1dca855cf98>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(array_n, array_expected_man_days)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- It looks like somewhere between 300 and 400 this function is maximized"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\frac{d}{dn}n\\cdot365\\cdot(364/365)^{n} = (364^{n})\\cdot(365^{1-n})\\cdot(1-n\\cdot\\log(365/364))\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\implies 0 = (364^{n})\\cdot(365^{1-n})\\cdot(1-n\\cdot\\log(365/364))\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\implies n = (-2\\log(2) + \\log(5) - \\log(7) - \\log(13) + \\log(73))^{-1} \\approx 364.49\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- So, it looks like **the ideal number of workers around 364**\n",
    "    - Let's derive the same number using a loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(365, 48943.523805351324)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max_man_days = 0\n",
    "max_n = 0\n",
    "\n",
    "for n in range(1, 1000):\n",
    "    E = n*365*((364/365)**n)\n",
    "    if E > max_man_days:\n",
    "        max_man_days = E\n",
    "        max_n = n\n",
    "max_n, max_man_days"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Ties out (pretty much)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_____\n",
    "\n",
    "- Let's simulate a couple $n$ values and try to tie out our result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sim(n, n_trials):\n",
    "    array_random = np.random.randint(365, size=(n, n_trials))\n",
    "    n_unique = pd.DataFrame(array_random).nunique()\n",
    "    return np.mean(n*(365 - n_unique))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "list_results = []\n",
    "\n",
    "for n in array_n[::20]:\n",
    "    list_results.append(sim(n, 10000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1dcaa238ef0>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(array_n, array_expected_man_days)\n",
    "plt.scatter(array_n[::20], list_results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Eyyy"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
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