Done puzzle 31

diff --git a/euler31.ipynb b/euler31.ipynb
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+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "true"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "require 'set'\n",
+    "require 'awesome_print'"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[1, 2, 5, 10, 20, 50, 100, 200]"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "ways = {[0, 0] => 1}\n",
+    "coins = [1,2,5,10,20,50,100,200]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{[0, 0]=>1}"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "ways"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[1, 2, 5, 10, 20, 50, 100]"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "coins[0...-1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       ":change_count"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "def change_count(coins, ncoins, total)\n",
+    "  puts(\"#{coins[0...ncoins]} coins finding #{total}\")\n",
+    "  if total == 0\n",
+    "    1\n",
+    "  elsif total < 0\n",
+    "    0\n",
+    "  elsif ncoins < 0 && total > 0\n",
+    "    0\n",
+    "  else\n",
+    "    change_count(coins, ncoins-1, total) + change_count(coins, ncoins, total-coins[ncoins])   \n",
+    "  end\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[1, 2, 5] coins finding 5\n",
+      "[1, 2] coins finding 5\n",
+      "[1] coins finding 5\n",
+      "[] coins finding 5\n",
+      "[1, 2, 5, 10, 20, 50, 100] coins finding 5\n",
+      "[] coins finding 4\n",
+      "[1, 2, 5, 10, 20, 50, 100] coins finding 4\n",
+      "[] coins finding 3\n",
+      "[1, 2, 5, 10, 20, 50, 100] coins finding 3\n",
+      "[] coins finding 2\n",
+      "[1, 2, 5, 10, 20, 50, 100] coins finding 2\n",
+      "[] coins finding 1\n",
+      "[1, 2, 5, 10, 20, 50, 100] coins finding 1\n",
+      "[] coins finding 0\n",
+      "[1] coins finding 3\n",
+      "[] coins finding 3\n",
+      "[1, 2, 5, 10, 20, 50, 100] coins finding 3\n",
+      "[] coins finding 2\n",
+      "[1, 2, 5, 10, 20, 50, 100] coins finding 2\n",
+      "[] coins finding 1\n",
+      "[1, 2, 5, 10, 20, 50, 100] coins finding 1\n",
+      "[] coins finding 0\n",
+      "[1] coins finding 1\n",
+      "[] coins finding 1\n",
+      "[1, 2, 5, 10, 20, 50, 100] coins finding 1\n",
+      "[] coins finding 0\n",
+      "[1] coins finding -1\n",
+      "[1, 2] coins finding 0\n",
+      "[1, 2, 5] coins finding -5\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "4"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "change_count(coins, 3, 5)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       ":change_count_dp"
+      ]
+     },
+     "execution_count": 40,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "def change_count_dp(coins, total, debug: false)\n",
+    "  ncoins = coins.length - 1\n",
+    "  ways = {}\n",
+    "  (0..total).each do |t|\n",
+    "    (0..ncoins).each do |n|\n",
+    "      ways[[n, t]] = 1\n",
+    "    end\n",
+    "  end\n",
+    "  \n",
+    "  (1..total).each do |t|\n",
+    "    (0..ncoins).each do |n|\n",
+    "      # including this coin\n",
+    "      if t >= coins[n]\n",
+    "        including = ways[[n, t-coins[n]]]\n",
+    "      else\n",
+    "        including = 0\n",
+    "      end\n",
+    "      \n",
+    "      # excluding this coin\n",
+    "      if n >= 1\n",
+    "        excluding = ways[[n-1, t]]\n",
+    "      else\n",
+    "        excluding = 0\n",
+    "      end\n",
+    "      \n",
+    "      puts \"n: #{n} (#{coins[n]}p), t: #{t}, inc: #{including}, exc: #{excluding}\" if debug\n",
+    "      ways[[n, t]] = including + excluding\n",
+    "    end\n",
+    "  end\n",
+    "  \n",
+    "  ways[[ncoins, total]]\n",
+    "  # ways\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[0, 1, 2, 3, 4, 5, 6, 7, 8]"
+      ]
+     },
+     "execution_count": 41,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(0..8).to_a"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "n: 0 (1p), t: 1, inc: 1, exc: 0\n",
+      "n: 1 (2p), t: 1, inc: 0, exc: 1\n",
+      "n: 2 (5p), t: 1, inc: 0, exc: 1\n",
+      "n: 3 (10p), t: 1, inc: 0, exc: 1\n",
+      "n: 4 (20p), t: 1, inc: 0, exc: 1\n",
+      "n: 5 (50p), t: 1, inc: 0, exc: 1\n",
+      "n: 6 (100p), t: 1, inc: 0, exc: 1\n",
+      "n: 7 (200p), t: 1, inc: 0, exc: 1\n",
+      "n: 0 (1p), t: 2, inc: 1, exc: 0\n",
+      "n: 1 (2p), t: 2, inc: 1, exc: 1\n",
+      "n: 2 (5p), t: 2, inc: 0, exc: 2\n",
+      "n: 3 (10p), t: 2, inc: 0, exc: 2\n",
+      "n: 4 (20p), t: 2, inc: 0, exc: 2\n",
+      "n: 5 (50p), t: 2, inc: 0, exc: 2\n",
+      "n: 6 (100p), t: 2, inc: 0, exc: 2\n",
+      "n: 7 (200p), t: 2, inc: 0, exc: 2\n",
+      "n: 0 (1p), t: 3, inc: 1, exc: 0\n",
+      "n: 1 (2p), t: 3, inc: 1, exc: 1\n",
+      "n: 2 (5p), t: 3, inc: 0, exc: 2\n",
+      "n: 3 (10p), t: 3, inc: 0, exc: 2\n",
+      "n: 4 (20p), t: 3, inc: 0, exc: 2\n",
+      "n: 5 (50p), t: 3, inc: 0, exc: 2\n",
+      "n: 6 (100p), t: 3, inc: 0, exc: 2\n",
+      "n: 7 (200p), t: 3, inc: 0, exc: 2\n",
+      "n: 0 (1p), t: 4, inc: 1, exc: 0\n",
+      "n: 1 (2p), t: 4, inc: 2, exc: 1\n",
+      "n: 2 (5p), t: 4, inc: 0, exc: 3\n",
+      "n: 3 (10p), t: 4, inc: 0, exc: 3\n",
+      "n: 4 (20p), t: 4, inc: 0, exc: 3\n",
+      "n: 5 (50p), t: 4, inc: 0, exc: 3\n",
+      "n: 6 (100p), t: 4, inc: 0, exc: 3\n",
+      "n: 7 (200p), t: 4, inc: 0, exc: 3\n",
+      "n: 0 (1p), t: 5, inc: 1, exc: 0\n",
+      "n: 1 (2p), t: 5, inc: 2, exc: 1\n",
+      "n: 2 (5p), t: 5, inc: 1, exc: 3\n",
+      "n: 3 (10p), t: 5, inc: 0, exc: 4\n",
+      "n: 4 (20p), t: 5, inc: 0, exc: 4\n",
+      "n: 5 (50p), t: 5, inc: 0, exc: 4\n",
+      "n: 6 (100p), t: 5, inc: 0, exc: 4\n",
+      "n: 7 (200p), t: 5, inc: 0, exc: 4\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "4"
+      ]
+     },
+     "execution_count": 45,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "change_count_dp(coins, 5, debug: true)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 43,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "73682"
+      ]
+     },
+     "execution_count": 43,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "change_count_dp(coins, 200)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Ruby 2.4.0",
+   "language": "ruby",
+   "name": "ruby"
+  },
+  "language_info": {
+   "file_extension": ".rb",
+   "mimetype": "application/x-ruby",
+   "name": "ruby",
+   "version": "2.4.0"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}