Adding problem 15 as a JN.

problems/015_problem/015_problem.ipynb

@@ -0,0 +1,73 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Problem 15:\n",
+    " \n",
+    "### [Euler Project #15](https://projecteuler.net/problem=15)\n",
+    " \n",
+    "### Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.\n",
+    "\n",
+    "### How many such routes are there through a 20×20 grid?\n",
+    "\n",
+    "---"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Let's try to map the example cases, by assigning a binary value to RIGHT and DOWN moves.\n",
+    "\n",
+    " 0 = R <br>\n",
+    " 1 = D\n",
+    "\n",
+    " 0 0 1 1 <br>\n",
+    " 0 1 0 1 <br>\n",
+    " 0 1 1 0 <br>\n",
+    " 1 0 0 1 <br>\n",
+    " 1 0 1 0 <br>\n",
+    " 1 1 0 0 <br>\n",
+    "\n",
+    "### A couple things that shake out of this,\n",
+    "1. The total length of a sequence of moves is the equal to Length + Width of the grid.\n",
+    "2. Each unique sequence of moves has a twin which is a mirror across the diagonal.\n",
+    "3. Each valid sequence has an equal number of RIGHT and DOWN moves.\n",
+    "\n",
+    "### I'm sure there is some combinatorial mathematics that describes how to do this analytically, but I'd rather practice programming a loop, than researching an elegant solution. \n",
+    "\n",
+    "---"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
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+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
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+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
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+ "nbformat": 4,
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+}