diff --git a/grid.ipynb b/grid.ipynb
index 4e3bbd7e5..77d1cf49a 100644
--- a/grid.ipynb
+++ b/grid.ipynb
@@ -1,26 +1,189 @@
 {
  "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "collapsed": false,
+    "deletable": true,
+    "editable": true
+   },
+   "source": [
+    "# Grid\n",
+    "\n",
+    "The functions here are used often when dealing with 2D grids (like in TicTacToe).\n",
+    "\n",
+    "### Distance\n",
+    "\n",
+    "The function returns the Euclidean Distance between two points in the 2D space."
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 6,
    "metadata": {
-    "collapsed": false
+    "collapsed": true,
+    "deletable": true,
+    "editable": true
    },
    "outputs": [],
    "source": [
-    "import grid\n",
+    "import math\n",
     "\n",
-    "print(grid.distance_squared((1, 2), (5, 5)))"
+    "def distance(a, b):\n",
+    "    \"\"\"The distance between two (x, y) points.\"\"\"\n",
+    "    return math.hypot((a[0] - b[0]), (a[1] - b[1]))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "deletable": true,
+    "editable": true
+   },
+   "source": [
+    "For example:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": false,
+    "deletable": true,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "5.0\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(distance((1, 2), (5, 5)))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "deletable": true,
+    "editable": true
+   },
+   "source": [
+    "### Distance Squared\n",
+    "\n",
+    "This function returns the square of the distance between two points."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": true,
+    "deletable": true,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "def distance_squared(a, b):\n",
+    "    \"\"\"The square of the distance between two (x, y) points.\"\"\"\n",
+    "    return (a[0] - b[0])**2 + (a[1] - b[1])**2"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "deletable": true,
+    "editable": true
+   },
+   "source": [
+    "For example:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": false,
+    "deletable": true,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "25\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(distance_squared((1, 2), (5, 5)))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "deletable": true,
+    "editable": true
+   },
+   "source": [
+    "### Vector Clip\n",
+    "\n",
+    "With this function we can make sure the values of a vector are within a given range. It takes as arguments three vectors: the vector to clip (`vector`), a vector containing the lowest values allowed (`lowest`) and a vector for the highest values (`highest`). All these vectors are of the same length. If a value `v1` in `vector` is lower than the corresponding value `v2` in `lowest`, then we set `v1` to `v2`. Similarly we \"clip\" the values exceeding the `highest` values."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
    "metadata": {
     "collapsed": true
    },
    "outputs": [],
-   "source": []
+   "source": [
+    "from utils import clip\n",
+    "\n",
+    "def vector_clip(vector, lowest, highest):\n",
+    "    \"\"\"Return vector, except if any element is less than the corresponding\n",
+    "    value of lowest or more than the corresponding value of highest, clip to\n",
+    "    those values.\"\"\"\n",
+    "    return type(vector)(map(clip, vector, lowest, highest))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "For example:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(0, 9)\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(vector_clip((-1, 10), (0, 0), (9, 9)))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The vector we wanted to clip was the tuple (-1, 10). The lowest allowed values were (0, 0) and the highest (9, 9). So, the result is the tuple (0,9)."
+   ]
   }
  ],
  "metadata": {
@@ -39,7 +202,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.5.1"
+   "version": "3.5.2"
   }
  },
  "nbformat": 4,