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problems/incomplete/015_problem/015_problem.ipynb

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+{
+ "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.<br>\n",
+    "    1. So, for a 20x20, each sequence will be 40 moves in length.\n",
+    "    1. That could 2**40 possible combinations, most of which will not be valid.\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. That will require some research, so I'll save this problem for another day.\n",
+    "\n",
+    "---"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
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problems/incomplete/015_problem/015_problem.py

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+# Problem 15:
+# 
+# [Euler Project #15](https://projecteuler.net/problem=15)
+# 
+# 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.
+# 
+# How many such routes are there through a 20×20 grid?
+# 
+# ---
+
+# Let's try to map the example cases, by assigning a binary value to RIGHT and DOWN moves.
+
+# 0 = R
+# 1 = D
+#
+# 0 0 1 1
+# 0 1 0 1 
+# 0 1 1 0
+# 1 0 0 1
+# 1 0 1 0
+# 1 1 0 0
+
+# A couple things that shake out of this,
+# 1. The total length of a sequence of moves is the equal to Length + Width of the grid.
+# 2. Each unique sequence of moves has a twin which is a mirror across the diagonal.
+# 3. Each valid sequence has an equal number of RIGHT and DOWN moves.
+
+# 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. 
+
+length=20
+width=20
+move_sequence_length=length+width
+
+count=0