100 sum random.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import pandas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "trials = []\n",
    "for i in range(1000000):\n",
    "    _ = sorted([random.randint(1,100) for j in range(9)])\n",
    "    trial = []\n",
    "    for j in range(8):\n",
    "        trial.append(_[j+1] - _[j])\n",
    "    trial.append(_[0])\n",
    "    trial.append(100-_[8])\n",
    "    assert(sum(trial) == 100)\n",
    "    trials += trial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x117794da0>]],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1176160f0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "pandas.DataFrame(trials).hist(bins=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4073731"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(i >= 10 for i in trials)/10000000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python (3.6, System)",
   "language": "python",
   "name": "py36"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}