David's Fruit Problem.ipynb

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  {
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   "source": [
    "Using a contraint solver to solve my friend David's son's ridiculously hard maths problem.\n",
    "\n",
    "![The Problem](davids-fruit-problem.jpg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from constraint import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "problem = Problem()\n",
    "problem.addVariable(\"pear\", range(1, 9))\n",
    "problem.addVariable(\"kiwi\", range(1, 9))\n",
    "problem.addVariable(\"banana\", range(1, 9))\n",
    "problem.addVariable(\"apple\", range(1, 9))\n",
    "problem.addVariable(\"orange\", range(1, 9))\n",
    "problem.addVariable(\"cherry\", range(1, 9))\n",
    "problem.addVariable(\"strawberry\", range(1, 9))\n",
    "problem.addVariable(\"melon\", range(1, 9))\n",
    "problem.addVariable(\"watermelon\", range(1, 9))\n",
    "\n",
    "problem.addConstraint(\n",
    "    lambda pear, kiwi, banana, apple: pear*(kiwi-banana) - apple == banana, \n",
    "    (\"pear\", \"kiwi\", \"banana\", \"apple\"))\n",
    "problem.addConstraint(\n",
    "    lambda orange, pear, cherry, kiwi: orange/pear + cherry - kiwi == kiwi, \n",
    "    (\"orange\", \"pear\", \"cherry\", \"kiwi\"))\n",
    "problem.addConstraint(\n",
    "    lambda strawberry, pear, apple, melon: strawberry*strawberry/pear + apple == melon, \n",
    "    (\"strawberry\", \"pear\", \"apple\", \"melon\"))\n",
    "problem.addConstraint(\n",
    "    lambda melon, kiwi, pear, banana, watermelon: (melon+kiwi)/pear + banana == watermelon, \n",
    "    (\"melon\", \"kiwi\", \"pear\", \"banana\", \"watermelon\"))\n",
    "\n",
    "solutions = problem.getSolutions()"
   ]
  },
  {
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   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(solutions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{'pear': 2,\n",
       "  'kiwi': 5,\n",
       "  'apple': 1,\n",
       "  'banana': 3,\n",
       "  'melon': 3,\n",
       "  'strawberry': 2,\n",
       "  'watermelon': 7,\n",
       "  'cherry': 8,\n",
       "  'orange': 4},\n",
       " {'pear': 2,\n",
       "  'kiwi': 5,\n",
       "  'apple': 1,\n",
       "  'banana': 3,\n",
       "  'melon': 3,\n",
       "  'strawberry': 2,\n",
       "  'watermelon': 7,\n",
       "  'cherry': 7,\n",
       "  'orange': 6},\n",
       " {'pear': 2,\n",
       "  'kiwi': 5,\n",
       "  'apple': 1,\n",
       "  'banana': 3,\n",
       "  'melon': 3,\n",
       "  'strawberry': 2,\n",
       "  'watermelon': 7,\n",
       "  'cherry': 6,\n",
       "  'orange': 8},\n",
       " {'pear': 2,\n",
       "  'kiwi': 4,\n",
       "  'apple': 2,\n",
       "  'banana': 2,\n",
       "  'melon': 4,\n",
       "  'strawberry': 2,\n",
       "  'watermelon': 6,\n",
       "  'cherry': 7,\n",
       "  'orange': 2},\n",
       " {'pear': 2,\n",
       "  'kiwi': 4,\n",
       "  'apple': 2,\n",
       "  'banana': 2,\n",
       "  'melon': 4,\n",
       "  'strawberry': 2,\n",
       "  'watermelon': 6,\n",
       "  'cherry': 6,\n",
       "  'orange': 4},\n",
       " {'pear': 2,\n",
       "  'kiwi': 4,\n",
       "  'apple': 2,\n",
       "  'banana': 2,\n",
       "  'melon': 4,\n",
       "  'strawberry': 2,\n",
       "  'watermelon': 6,\n",
       "  'cherry': 5,\n",
       "  'orange': 6},\n",
       " {'pear': 2,\n",
       "  'kiwi': 4,\n",
       "  'apple': 2,\n",
       "  'banana': 2,\n",
       "  'melon': 4,\n",
       "  'strawberry': 2,\n",
       "  'watermelon': 6,\n",
       "  'cherry': 4,\n",
       "  'orange': 8},\n",
       " {'pear': 2,\n",
       "  'kiwi': 3,\n",
       "  'apple': 3,\n",
       "  'banana': 1,\n",
       "  'melon': 5,\n",
       "  'strawberry': 2,\n",
       "  'watermelon': 5,\n",
       "  'cherry': 5,\n",
       "  'orange': 2},\n",
       " {'pear': 2,\n",
       "  'kiwi': 3,\n",
       "  'apple': 3,\n",
       "  'banana': 1,\n",
       "  'melon': 5,\n",
       "  'strawberry': 2,\n",
       "  'watermelon': 5,\n",
       "  'cherry': 4,\n",
       "  'orange': 4},\n",
       " {'pear': 2,\n",
       "  'kiwi': 3,\n",
       "  'apple': 3,\n",
       "  'banana': 1,\n",
       "  'melon': 5,\n",
       "  'strawberry': 2,\n",
       "  'watermelon': 5,\n",
       "  'cherry': 3,\n",
       "  'orange': 6},\n",
       " {'pear': 2,\n",
       "  'kiwi': 3,\n",
       "  'apple': 3,\n",
       "  'banana': 1,\n",
       "  'melon': 5,\n",
       "  'strawberry': 2,\n",
       "  'watermelon': 5,\n",
       "  'cherry': 2,\n",
       "  'orange': 8},\n",
       " {'pear': 1,\n",
       "  'kiwi': 4,\n",
       "  'apple': 2,\n",
       "  'banana': 1,\n",
       "  'melon': 3,\n",
       "  'strawberry': 1,\n",
       "  'watermelon': 8,\n",
       "  'cherry': 7,\n",
       "  'orange': 1},\n",
       " {'pear': 1,\n",
       "  'kiwi': 4,\n",
       "  'apple': 2,\n",
       "  'banana': 1,\n",
       "  'melon': 3,\n",
       "  'strawberry': 1,\n",
       "  'watermelon': 8,\n",
       "  'cherry': 6,\n",
       "  'orange': 2},\n",
       " {'pear': 1,\n",
       "  'kiwi': 4,\n",
       "  'apple': 2,\n",
       "  'banana': 1,\n",
       "  'melon': 3,\n",
       "  'strawberry': 1,\n",
       "  'watermelon': 8,\n",
       "  'cherry': 5,\n",
       "  'orange': 3},\n",
       " {'pear': 1,\n",
       "  'kiwi': 4,\n",
       "  'apple': 2,\n",
       "  'banana': 1,\n",
       "  'melon': 3,\n",
       "  'strawberry': 1,\n",
       "  'watermelon': 8,\n",
       "  'cherry': 4,\n",
       "  'orange': 4},\n",
       " {'pear': 1,\n",
       "  'kiwi': 4,\n",
       "  'apple': 2,\n",
       "  'banana': 1,\n",
       "  'melon': 3,\n",
       "  'strawberry': 1,\n",
       "  'watermelon': 8,\n",
       "  'cherry': 3,\n",
       "  'orange': 5},\n",
       " {'pear': 1,\n",
       "  'kiwi': 4,\n",
       "  'apple': 2,\n",
       "  'banana': 1,\n",
       "  'melon': 3,\n",
       "  'strawberry': 1,\n",
       "  'watermelon': 8,\n",
       "  'cherry': 2,\n",
       "  'orange': 6},\n",
       " {'pear': 1,\n",
       "  'kiwi': 4,\n",
       "  'apple': 2,\n",
       "  'banana': 1,\n",
       "  'melon': 3,\n",
       "  'strawberry': 1,\n",
       "  'watermelon': 8,\n",
       "  'cherry': 1,\n",
       "  'orange': 7},\n",
       " {'pear': 1,\n",
       "  'kiwi': 3,\n",
       "  'apple': 1,\n",
       "  'banana': 1,\n",
       "  'melon': 2,\n",
       "  'strawberry': 1,\n",
       "  'watermelon': 6,\n",
       "  'cherry': 5,\n",
       "  'orange': 1},\n",
       " {'pear': 1,\n",
       "  'kiwi': 3,\n",
       "  'apple': 1,\n",
       "  'banana': 1,\n",
       "  'melon': 2,\n",
       "  'strawberry': 1,\n",
       "  'watermelon': 6,\n",
       "  'cherry': 4,\n",
       "  'orange': 2},\n",
       " {'pear': 1,\n",
       "  'kiwi': 3,\n",
       "  'apple': 1,\n",
       "  'banana': 1,\n",
       "  'melon': 2,\n",
       "  'strawberry': 1,\n",
       "  'watermelon': 6,\n",
       "  'cherry': 3,\n",
       "  'orange': 3},\n",
       " {'pear': 1,\n",
       "  'kiwi': 3,\n",
       "  'apple': 1,\n",
       "  'banana': 1,\n",
       "  'melon': 2,\n",
       "  'strawberry': 1,\n",
       "  'watermelon': 6,\n",
       "  'cherry': 2,\n",
       "  'orange': 4},\n",
       " {'pear': 1,\n",
       "  'kiwi': 3,\n",
       "  'apple': 1,\n",
       "  'banana': 1,\n",
       "  'melon': 2,\n",
       "  'strawberry': 1,\n",
       "  'watermelon': 6,\n",
       "  'cherry': 1,\n",
       "  'orange': 5}]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solutions"
   ]
  }
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