diff --git a/Mean Misanthrope Density.ipynb b/Mean Misanthrope Density.ipynb
index 7ee659c..dd0996a 100644
--- a/Mean Misanthrope Density.ipynb	
+++ b/Mean Misanthrope Density.ipynb	
@@ -25,17 +25,17 @@
     "     \n",
     "Now the first person chooses one of the four houses (which are all acceptable). We'll indicate an occupied house by a `1`, so the four equiprobable choices are:\n",
     "\n",
-    "     1...\n",
-    "     .1..\n",
-    "     ..1.\n",
-    "     ...1\n",
+    "     Choice 0: 1...\n",
+    "     Choice 1: .1..\n",
+    "     Choice 2: ..1.\n",
+    "     Choice 3: ...1\n",
     "     \n",
     "When a house is occupied, any adjacent houses become unacceptable. We'll indicate that with a `0`:\n",
     "\n",
-    "     10..\n",
-    "     010.\n",
-    "     .010\n",
-    "     ..01\n",
+    "     Choice 0: 10..\n",
+    "     Choice 1: 010.\n",
+    "     Choice 2: .010\n",
+    "     Choice 3: ..01\n",
     "     \n",
     "In all four cases, a second occupant has a place to move in, but then there is no place for a third occupant. \n",
     "The occupancy is 2 in all cases, and thus the *expected occpancy* is 2. The occupancy fraction, or *density*, is 2/*N* = 2/4 = 1/2.\n",
@@ -45,35 +45,35 @@
     "\n",
     "With *N*=7 houses, there are 7 equiprobable choices for the first occupant:\n",
     "\n",
-    "     10.....\n",
-    "     010....\n",
-    "     .010...\n",
-    "     ..010..\n",
-    "     ...010.\n",
-    "     ....010\n",
-    "     .....01\n",
+    "     Choice 0: 10.....\n",
+    "     Choice 1: 010....\n",
+    "     Choice 2: .010...\n",
+    "     Choice 3: ..010..\n",
+    "     Choice 4: ...010.\n",
+    "     Choice 5: ....010\n",
+    "     Choice 6: .....01\n",
     "     \n",
     "Now we'll add something new: the lengths of the **runs** of consecutive acceptable houses to the left and right of the chosen house:\n",
     "\n",
-    "     10..... runs = (0, 5)\n",
-    "     010.... runs = (0, 4)\n",
-    "     .010... runs = (1, 3)\n",
-    "     ..010.. runs = (2, 2)\n",
-    "     ...010. runs = (3, 1)\n",
-    "     ....010 runs = (4, 0)\n",
-    "     .....01 runs = (5, 0)\n",
+    "     Choice 0: 10..... runs = (0, 5)\n",
+    "     Choice 1: 010.... runs = (0, 4)\n",
+    "     Choice 2: .010... runs = (1, 3) \n",
+    "     Choice 3: ..010.. runs = (2, 2) \n",
+    "     Choice 4: ...010. runs = (3, 1) \n",
+    "     Choice 5: ....010 runs = (4, 0) \n",
+    "     Choice 6: .....01 runs = (5, 0) \n",
     "     \n",
     "# Defining `occ(n)`\n",
     "\n",
     "This gives me a key hint as to how to analyze the problem. I'll define `occ(n)` to be the expected number of occupied houses in a row of `n` houses. So:\n",
     "\n",
-    "     10..... runs = (0, 5); occupancy = occ(0) + 1 + occ(5)\n",
-    "     010.... runs = (0, 4); occupancy = occ(0) + 1 + occ(4)\n",
-    "     .010... runs = (1, 3); occupancy = occ(1) + 1 + occ(3)\n",
-    "     ..010.. runs = (2, 2); occupancy = occ(2) + 1 + occ(2)\n",
-    "     ...010. runs = (3, 1); occupancy = occ(3) + 1 + occ(1)\n",
-    "     ....010 runs = (4, 0); occupancy = occ(4) + 1 + occ(0)\n",
-    "     .....01 runs = (5, 0); occupancy = occ(5) + 1 + occ(0)     \n",
+    "     Choice 0: 10..... runs = (0, 5); occupancy = occ(0) + 1 + occ(5)\n",
+    "     Choice 1: 010.... runs = (0, 4); occupancy = occ(0) + 1 + occ(4)\n",
+    "     Choice 2: .010... runs = (1, 3); occupancy = occ(1) + 1 + occ(3)\n",
+    "     Choice 3: ..010.. runs = (2, 2); occupancy = occ(2) + 1 + occ(2)\n",
+    "     Choice 4: ...010. runs = (3, 1); occupancy = occ(3) + 1 + occ(1)\n",
+    "     Choice 5: ....010 runs = (4, 0); occupancy = occ(4) + 1 + occ(0)\n",
+    "     Choice 6: .....01 runs = (5, 0); occupancy = occ(5) + 1 + occ(0)     \n",
     "     \n",
     "So we can say that `occ(n)` is:\n",
     "\n",
@@ -88,9 +88,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "from statistics import mean\n",
@@ -115,44 +113,47 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Let's check that `occ(4)` is 2, as we computed it should be:"
+    "Let's check that `occ(4)` is 2, as we computed it should be, and for other small values, up to 7:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 2,
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "2.0"
+       "{0: 0,\n",
+       " 1: 1,\n",
+       " 2: 1,\n",
+       " 3: 1.6666666666666667,\n",
+       " 4: 2,\n",
+       " 5: 2.466666666666667,\n",
+       " 6: 2.888888888888889,\n",
+       " 7: 3.323809523809524}"
       ]
      },
-     "execution_count": 30,
+     "execution_count": 2,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "occ(4)"
+    "{n: occ(n) for n in range(8)}"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "And that `runs(7)` is what we described above:"
+    "That looks good, although I can't prove the value above 4 are ccorrect. Now check that `runs(7)` is what we described above:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 3,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -173,75 +174,15 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Let's check on `n = 7`:"
+    "# Dynamic Programming Version of `occ`\n",
+    "\n",
+    "The computation of `occ(n)` makes multiple calls to `occ(n-1), occ(n-2),` etc. To avoid re-computing the same calls over and over, we will modify `occ` to save previous results using [dynamic programming](https://en.wikipedia.org/wiki/Dynamic_programming). I could implement that in one line with the decorator [`@functools.lru_cache`](https://docs.python.org/3/library/functools.html#functools.lru_cache), but then I would have to worry about the recursion limit. Instead I will explicitly manage a list, `cache`, such that `cache[n]` holds `occ(n)`:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 4,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "3.3238095238095235"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "occ(7)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "0.47482993197278905"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "density(7)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
    "metadata": {},
-   "source": [
-    "That seems reasonable, but I don't know for sure that it is correct. "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Dynamic Programming Version of `occ`\n",
-    "\n",
-    "The computation of `occ(n)` makes multiple calls to `occ(n-1), occ(n-2),` etc. To avoid re-computing the same calls over and over, we will modify `occ` to save previous results using [dynamic programming](https://en.wikipedia.org/wiki/Dynamic_programming). I could implement that in one line with the decorator [`@functools.lru_cache`](https://docs.python.org/3/library/functools.html#functools.lru_cache), but instead I will explicitly manage a list, `cache`, such that `cache[n]` holds `occ(n)`:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {
-    "collapsed": false
-   },
    "outputs": [],
    "source": [
     "def occ(n, cache=[0, 1]):\n",
@@ -262,10 +203,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 5,
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -273,7 +212,7 @@
        "True"
       ]
      },
-     "execution_count": 32,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -284,46 +223,42 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 6,
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "0.47482993197278905"
+       "3.323809523809524"
       ]
      },
-     "execution_count": 33,
+     "execution_count": 6,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "density(7)"
+    "occ(7)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Let's make sure the caching makes computation faster the second time:"
+    "Let's make sure the caching makes computation pretty fast the first time, and *very* fast the second time:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 7,
+   "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 6.23 s, sys: 115 ms, total: 6.34 s\n",
-      "Wall time: 6.97 s\n"
+      "CPU times: user 2.68 s, sys: 13.5 ms, total: 2.7 s\n",
+      "Wall time: 2.71 s\n"
      ]
     },
     {
@@ -332,7 +267,7 @@
        "864.9617138385324"
       ]
      },
-     "execution_count": 9,
+     "execution_count": 7,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -343,17 +278,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 8,
+   "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 5 µs, sys: 0 ns, total: 5 µs\n",
-      "Wall time: 9.06 µs\n"
+      "CPU times: user 4 µs, sys: 0 ns, total: 4 µs\n",
+      "Wall time: 5.01 µs\n"
      ]
     },
     {
@@ -362,7 +295,7 @@
        "864.9617138385324"
       ]
      },
-     "execution_count": 10,
+     "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -382,14 +315,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 9,
+   "metadata": {},
    "outputs": [],
    "source": [
     "%matplotlib inline\n",
     "import matplotlib.pyplot as plt\n",
+    "plt.style.use('fivethirtyeight')\n",
     "\n",
     "def plot_density(ns):\n",
     "    \"Plot density(n) for each n in the list of numbers ns.\"\n",
@@ -400,10 +332,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 10,
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -411,15 +341,15 @@
        "0.4353323288377046"
       ]
      },
-     "execution_count": 12,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     },
     {
      "data": {
-      "image/png": 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lVemQcCVhZpZWpUPClYSZWVqVDwlXEmZm6VQ6JNzdZGaWVqVDwt1NZmZpVT4kXEmYmaVT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\ngg==\n",
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OwbKXLl2Co6Ojxo+TkxNOnz5t8vX0vYfYxUEEx3Yi9Oqi2UPkc0QiImGw+uTe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\nEQFgIBIREQFgIBIREQFgIBIREQEA/h/5AVenm8CM8AAAAABJRU5ErkJggg==\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1043b8eb8>"
+       "<matplotlib.figure.Figure at 0x11202c0b8>"
       ]
      },
      "metadata": {},
@@ -439,10 +369,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 11,
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -450,15 +378,15 @@
        "0.46203174603174607"
       ]
      },
-     "execution_count": 13,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     },
     {
      "data": {
-      "image/png": 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RE7PpJ/jatWubqw6Hp1YpTQLwhEaLv7TzkLAiIiK6GZwJpokspkRjT1AiIqfWYAB+8803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\nQmCC\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x10c5ac940>"
+       "<matplotlib.figure.Figure at 0x1120519e8>"
       ]
      },
      "metadata": {},
@@ -478,10 +406,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 12,
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -489,15 +415,15 @@
        "0.43240754751464183"
       ]
      },
-     "execution_count": 14,
+     "execution_count": 12,
      "metadata": {},
      "output_type": "execute_result"
     },
     {
      "data": {
-      "image/png": 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HDnS9nnM4MZbDCcjMmqZVR2aV0Ros4hxDLZH6i6hmZsNE9deNGz0K7pprLm7o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\nIDMzK4UTkJmZlcIJyMzMSvH/AUDe4DLY0Sj0AAAAAElFTkSuQmCC\n",
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HHntMeP3EiRPCQyXozo22ZhgTEfUHBoXx4sWL8e6778LNzQ1PPPEEUlNTYWpq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\nYII=\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x10ca875c0>"
+       "<matplotlib.figure.Figure at 0x1149702e8>"
       ]
      },
      "metadata": {},
@@ -523,7 +449,7 @@
     "\n",
     "# lim <sub>n &rarr; &infin;</sub> density(n)\n",
     "\n",
-    "[Thes puzzle](http://fivethirtyeight.com/features/can-you-solve-the-puzzle-of-your-misanthropic-neighbors/)\n",
+    "[The puzzle](http://fivethirtyeight.com/features/can-you-solve-the-puzzle-of-your-misanthropic-neighbors/)\n",
     "is to figure out the limit of `density(n)` as `n` goes to infinity. The plot above makes it look like  0.432+something, but we can't answer the question just by plotting;  we'll need to switch modes from *computational* thinking to *mathematical* thinking.\n",
     "\n",
     "At this point I started playing around with `density(n)`, looking at various values, differences of values, ratios of values, and ratios of differences of values, hoping to achieve some mathematical insight. Mostly I got dead ends.\n",
@@ -532,10 +458,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 13,
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -543,7 +467,7 @@
        "0.0014849853757253895"
       ]
      },
-     "execution_count": 15,
+     "execution_count": 13,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -563,10 +487,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 14,
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -574,7 +496,7 @@
        "0.0007424926878626947"
       ]
      },
-     "execution_count": 16,
+     "execution_count": 14,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -592,10 +514,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 15,
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -603,7 +523,7 @@
        "2.0"
       ]
      },
-     "execution_count": 17,
+     "execution_count": 15,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -621,10 +541,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 16,
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -632,7 +550,27 @@
        "2.0"
       ]
      },
-     "execution_count": 18,
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "n = 250; diff(n, 2*n) / diff(2*n, 4*n)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2.0"
+      ]
+     },
+     "execution_count": 17,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -641,28 +579,6 @@
     "n = 500; diff(n, 2*n) / diff(2*n, 4*n)"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "1.9999999999992524"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "n = 1000; diff(n, 2*n) / diff(2*n, 4*n)"
-   ]
-  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -682,24 +598,22 @@
     "\n",
     "    density(n) = A + B / n \n",
     "    \n",
-    "would fit the patterm.  I can try a `curve_fit` to estimate the parameters *A* and *B*:"
+    "would fit the patterm.  I can try a `scipy.optimize.curve_fit` to estimate the parameters *A* and *B*:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 18,
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([[  7.64810902e-34,  -2.42654280e-31],\n",
-       "       [ -2.42654280e-31,   4.67778766e-28]])"
+       "array([[  4.70916321e-33,  -1.30373854e-30],\n",
+       "       [ -1.30373854e-30,   1.44885627e-27]])"
       ]
      },
-     "execution_count": 20,
+     "execution_count": 18,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -707,7 +621,7 @@
    "source": [
     "from scipy.optimize import curve_fit\n",
     "\n",
-    "Ns = list(range(100, 10001, 100))\n",
+    "Ns = list(range(100, 5001, 100))\n",
     "\n",
     "def f(n, A, B): return A + B / n\n",
     "\n",
@@ -725,18 +639,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 19,
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "(0.43233235838169343, 0.29699707514520357)"
+       "(0.43233235838169332, 0.29699707514503415)"
       ]
      },
-     "execution_count": 21,
+     "execution_count": 19,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -754,10 +666,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 20,
+   "metadata": {},
    "outputs": [],
    "source": [
     "def estimated_density(n): return A + B / n"
@@ -772,18 +682,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 21,
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "3.8857805861880479e-16"
+       "6.106226635438361e-16"
       ]
      },
-     "execution_count": 23,
+     "execution_count": 21,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -801,7 +709,7 @@
     "\n",
     "We now have a plausible answer to the puzzle:\n",
     "\n",
-    "> lim<sub style=\"font-size:large\"> <tt>n</tt>&rarr;&infin;</sub> <tt>density(n) &cong; A = 0.43233235838169343</tt>"
+    "> lim<sub style=\"font-size:large\"> <tt>n</tt>&rarr;&infin;</sub> <tt>density(n) &cong; A = 0.43233235838169</tt>"
    ]
   },
   {
@@ -812,7 +720,7 @@
     "\n",
     "Theis answer is empirically strong (15 decimal places of accuracy) but theoretically weak: we don't have a **proof**, and we don't have an explanation for **why** the density function has this form. We need some more mathematical thinking. \n",
     "\n",
-    "I didn't have any ideas, so I looked to see if anyone else had written something about the number 0.43233235838169343. I tried several searches and found two interesting formulas:\n",
+    "I didn't have any ideas, so I looked to see if anyone else had written something about the number 0.432332358169 I tried several searches and found two interesting formulas:\n",
     "\n",
     "- Search: [`[0.4323323]`](https://www.google.com/search?q=0.4323323) Formula: `sinh(1) / exp(1)` [(Page)](http://arxiv.org/pdf/1310.4360.pdf)\n",
     "- Search: [`[0.432332358]`](https://www.google.com/search?q=0.432332358) Formula: `0.5(1-e^(-2))` [(Page)](http://www.actuarialoutpost.com/actuarial_discussion_forum/archive/index.php/t-52095.html)\n",
@@ -822,18 +730,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 22,
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "(0.43233235838169365, 0.43233235838169365, 0.43233235838169343)"
+       "(0.43233235838169365, 0.43233235838169365, 0.43233235838169332)"
       ]
      },
-     "execution_count": 24,
+     "execution_count": 22,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -844,8 +750,6 @@
     "S = sinh(1) / exp(1)\n",
     "E = 0.5 * (1 - e ** (-2))\n",
     "\n",
-    "assert S == E\n",
-    "\n",
     "S, E, A"
    ]
   },
@@ -933,9 +837,9 @@
     "\n",
     "Is our implementation of `occ(n)` correct? I think it is, but I can anticipate some objections and answer them:\n",
     "\n",
-    "- In `occ(n)`, is it ok to start from all empty houses, rather than considering layouts of partially-occupied houses? Yes, I think it is ok, because the problem states that initially all houses are empty, and each choice of a house breaks the street up into runs of acceptable houses, flanked by unacceptable houses. If we get the computation right for a run of `n` acceptable houses, then we can get the whole answer right. A key point is that the chosen first house breaks the row of houses into 2 runs of *acceptable* houses, not 2 runs of *unoccupied* houses. If it were unoccupied houses, then we would have to also keep track of whether there were occupied houses to the right and/or left of the runs. By considering runs of acceptable houses, eveything is clean and simple.\n",
+    "- *In `occ(n)`, is it ok to start from all empty houses, rather than considering layouts of partially-occupied houses?* Yes, because the problem states that initially all houses are empty, and each choice of a house breaks the street up into runs of acceptable houses, flanked by unacceptable houses. If we get the computation right for a run of `n` acceptable houses, then we can get the whole answer right. A key point is that the chosen first house breaks the row of houses into 2 runs of *acceptable* houses, not 2 runs of *unoccupied* houses. If it were unoccupied houses, then we would have to also keep track of whether there were occupied houses to the right and/or left of the runs. By considering runs of acceptable houses, eveything is clean and simple.\n",
     "\n",
-    "- In `occ(7)`, if the first house chosen is 2, that breaks the street up into runs of 1 and 3 acceptable houses. There is only one way to occupy the 1 house, but there are several ways to occupy the 3 houses. Shouldn't the average give more weight to the 3 houses, since there are more possibilities there? No, I don't think so. We are caclulating occupancy, and there is a specific number (5/3) which is the expected occupancy of 3 houses; it doesn't matter if there is one combination or a million combinations that contribute to that expected value, all that matters is what the expected value is.\n",
+    "- *In `occ(7)`, if the first house chosen is 2, that breaks the street up into runs of 1 and 3 acceptable houses. There is only one way to occupy the 1 house, but there are several ways to occupy the 3 houses. Shouldn't the average give more weight to the 3 houses, since there are more possibilities there?* No. We are caclulating occupancy, and there is a specific number (5/3) which is the expected occupancy of 3 houses; it doesn't matter if there is one combination or a million combinations that contribute to that expected value, all that matters is what the expected value is.\n",
     "\n",
     "\n"
    ]
@@ -948,19 +852,17 @@
     "\n",
     "\n",
     "A simulation can add credence to our implementation of `density(n)`, for two reasons:\n",
-    "- The code for the simulation can  have a more direct corresponance to the problem statement.\n",
+    "- The code for the simulation can  have a more direct correspondance to the problem statement.\n",
     "- When two very different implementations get the same result, that is evidence supporting both of them.\n",
     "\n",
     "\n",
-    "The simulation will start with an empty set of occupied houses. Following Lamping's suggestion, we sample <i>n</i> houses (to get a random ordering) and go through them, occupying just the ones that have no neighbor\" "
+    "The simulation will start with an empty set of occupied houses. We then go through the houses in random order, occupying just the ones that have no neighbor. (Note that `random.sample(range(n), n)` gives a random ordering of `range(n)`.)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 23,
+   "metadata": {},
    "outputs": [],
    "source": [
     "import random\n",
@@ -988,28 +890,27 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 24,
+   "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "  n   simul    density  estimated\n",
-      " 25   0.444    0.444    0.444\n",
-      " 50   0.438    0.438    0.438\n",
-      "100   0.435    0.435    0.435\n",
-      "200   0.434    0.434    0.434\n",
-      "400   0.433    0.433    0.433\n"
+      "   n   simulate  density   estimated\n",
+      "  10   0.4621    0.4620    0.4620\n",
+      "  25   0.4442    0.4442    0.4442\n",
+      "  50   0.4383    0.4383    0.4383\n",
+      " 100   0.4354    0.4353    0.4353\n",
+      " 200   0.4339    0.4338    0.4338\n",
+      " 400   0.4331    0.4331    0.4331\n"
      ]
     }
    ],
    "source": [
-    "print('  n   simul    density  estimated')\n",
-    "for n in (25, 50, 100, 200, 400):\n",
-    "    print('{:3}   {:.3}    {:.3}    {:.3}'\n",
+    "print('   n   simulate  density   estimated')\n",
+    "for n in (10, 25, 50, 100, 200, 400):\n",
+    "    print('{:4d}   {:.4f}    {:.4f}    {:.4f}'\n",
     "          .format(n, simulated_density(n), density(n), estimated_density(n)))"
    ]
   },
@@ -1017,17 +918,15 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We got perfect agreement (at least to 3 decimal places), suggesting that either our three implementations are all correct, or we've made  mistakes in all three. \n",
+    "We get good agreement (at least to 3 decimal places), suggesting that either our three implementations are all correct, or we've made  mistakes in all three. \n",
     "\n",
     "The `simulate` function can also give us insights when we look at the results it produces:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 25,
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -1035,7 +934,7 @@
        "[0, 2, 4, 6]"
       ]
      },
-     "execution_count": 27,
+     "execution_count": 25,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1053,24 +952,22 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 26,
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Counter({(0, 2, 4, 6): 3303,\n",
-       "         (0, 2, 5): 1255,\n",
-       "         (0, 3, 5): 959,\n",
-       "         (0, 3, 6): 783,\n",
-       "         (1, 3, 5): 1426,\n",
-       "         (1, 3, 6): 974,\n",
-       "         (1, 4, 6): 1300})"
+       "Counter({(0, 2, 4, 6): 3220,\n",
+       "         (0, 2, 5): 1214,\n",
+       "         (0, 3, 5): 1029,\n",
+       "         (0, 3, 6): 827,\n",
+       "         (1, 3, 5): 1417,\n",
+       "         (1, 3, 6): 976,\n",
+       "         (1, 4, 6): 1317})"
       ]
      },
-     "execution_count": 28,
+     "execution_count": 26,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1099,10 +996,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 27,
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -1110,7 +1005,7 @@
        "'ok'"
       ]
      },
-     "execution_count": 29,
+     "execution_count": 27,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1135,9 +1030,9 @@
     "    occupied = set(occupied) # coerce to set\n",
     "    for house in range(n):\n",
     "        if house in occupied:\n",
-    "            assert (house - 1) not in occupied and (house + 1) not in occupied\n",
+    "            assert not ((house - 1) in occupied or (house + 1) in occupied)\n",
     "        else:\n",
-    "            assert (house - 1) in occupied or (house + 1) in occupied\n",
+    "            assert      (house - 1) in occupied or (house + 1) in occupied\n",
     "\n",
     "test()"
    ]
@@ -1172,9 +1067,9 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.5.1"
+   "version": "3.5.3"
   }
  },
  "nbformat": 4,
- "nbformat_minor": 0
+ "nbformat_minor": 1
 }