analysis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot\n",
    "from collections import Counter\n",
    "\n",
    "pyplot.style.use(\"seaborn\")\n",
    "pyplot.rcParams['savefig.dpi'] = 200\n",
    "pyplot.rcParams[\"figure.autolayout\"] = True\n",
    "\n",
    "POSITIONS = list(\"12345678\")\n",
    "SYMBOLS = list(\"0123456789+-/*=\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generating possible answers\n",
    "\n",
    "I generated all possible answers using the code in `nerdle.py`. This should be the same as the possible nerdle answers, as the number generated (17723) is the same as the number of possible solutions mentioned on the nerdle website.\n",
    "\n",
    "Some rules are covered [in the nerdle faq](https://faqs.nerdlegame.com/), but here's a summary:\n",
    " - The result (after =) must be a positive integer or 0.\n",
    " - Division is treated as normal division (not integer division/no rounding).\n",
    " - Lone 0's are not allowed in the LHS.\n",
    " - Trailing 0's are not allowed anywhere.\n",
    " - Negative numbers cannot be used (and you cannot use + as a unary operator) anywhere.\n",
    " - Order of operations apply.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['1*1+9=10', '1*10-1=9', '1*10-2=8', '1*10-3=7', '1*10-4=6']\n",
      "17723\n"
     ]
    }
   ],
   "source": [
    "with open(\"all_answers.txt\", \"r\") as f:\n",
    "    data = f.read().splitlines()\n",
    "\n",
    "print(data[:5])\n",
    "print(len(data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('1', 2017), ('2', 1949), ('3', 1645), ('+', 1606), ('4', 1547)]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frequencies: dict[int, Counter[str, int]]= {}\n",
    "for equation in data:\n",
    "    for pos, char in enumerate(equation, 1):\n",
    "        frequencies.setdefault(pos, Counter())[char] += 1\n",
    "\n",
    "# frequencies[4] gives total counts for each symbol at the 4th position in the equation.\n",
    "frequencies[4].most_common(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Frequency of each symbol across all answers\n",
    "\n",
    "Shows the probability that, if you pick a random character from a random answer, it will be that symbol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lZ828ceNGXXPNNbrrrrt03XXX6f3331dFRcU5rW9hYaE6deqkBg0aaNiwYXrooYe0bdu2c348VPWzLx3fO3RqIbrQx1l8fLy+/PJLDRgwQFOnTtXhw4c9RRq/fuzBQbULCwvT/Pnz9cQTT+iFF15QeXm5HnzwQbVt21aSdMcddyghIUHh4eG69NJLPddLTEzUI488op49e+qyyy7Tdddd51k2Y8YMTZ06Vf369ZPL5VLfvn110003nfWlnPj4eO3du1cDBgyQMUbXXXedEhMTJR1/2aJ+/fqVXtY52eWXX64pU6bo/vvvV0VFhWrVqqWFCxd6/UtvxowZSklJ0euvvy6Xy6V+/fppwIABCgoK0owZMzR+/HjPm5Znz56t3/72t2c8PyIiQmPHjtWIESPUqFGjSntJThUXF6cRI0Zo+PDhCgoKktPp1LPPPlvlngvp+H00b948paam6qmnnlJoaKjmzZt31vvuqquu0r/+9S/16dNHtWvX1h/+8AfdcccdlW43NDRU8+fP17Rp0zRv3jxVVFRo1KhRateu3Vm322233ab9+/dr0KBBCgoK0u9//3ulpaWpfv36+p//+R/dcsstatCggRo2bKiYmBjt2rVL7du3P+O2O1c33HCDsrOz1bdvX9WpU0f169fX1KlTPcsHDBigd999V1dcccU53+YJv/nNb7RmzRrNmTNHtWvX1rx58+RwODRy5EhNnz5d/fv3V3l5uaKjozV58uQqb8fb9mzcuLFatWql8vJyXXLJJZKkli1bKiUlRQ8//LCMMXI4HFqwYEGVe25O6Nu3r9asWaM+ffooNDRU7du316FDhzyl82waNWqkkSNHatiwYapVq5ZCQkI0bdq0s+bfsGGD5/pn+9m/4YYbKt0v3rbLybd7qkceeUSpqamaM2eOgoODdf/99+uyyy7zun74dQgyZ9r3DvjJqlWr9Morr2jJkiU+nbt7924lJiZq1apVnpe9gBPKy8t1//3366abbvK8lwZAYOMlKtR4c+fO1ZAhQzR+/HjKDU6zY8cOtW/fXnXr1j3rnjMAgYU9OAAAwDrswQEAANah4AAAAOsEzKeoCgqK/B3hNA0b1tHBg0dq7PxAyFDT5wdCBn/PD4QM/p4fCBlq+vxAyODv+YGS4VSNG5/506zswTkLhyOkRs8PhAw1fX4gZPD3/EDI4O/5gZChps8PhAz+nh8oGc4VBQcAAFiHggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOAAAwDoUHAAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAQAA1qHgAAAA61BwAACAdSg4AADAOhQcAABgHYe/AwAAAN8bnpblkzmLJ3T1yZxTsQcHAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1KDgAAMA6FBwAAGAdCg4AALAOBQcAAFjHa8Fxu91KSkrS4MGDlZiYqF27dp12mcLCQvXs2VOlpaWSpKKiIt133326/fbbNXjwYH3xxRcXPzkAAEAVvBactWvXyuVyKTMzU2PGjFFaWlql5R999JGGDx+ugoICz3np6elq166d/u///k9PPvmkUlJSLn5yAACAKnj9Lqrc3FzFxcVJklq3bq38/PxKy4ODg5Wenq5bb73Vc96wYcMUFhYmSaqoqFB4ePjFzAwAAHBWXgtOcXGxnE6n53RISIjKy8vlcBy/amxs7GnXqVevniSpoKBAY8eO1aRJk7wGadiwjhyOkHMO7iuNG0fU6PmBkKGmzw+EDP6eHwgZ/D0/EDLU9PmBkMHf8y+EvzJ7LThOp1MlJSWe026321Nuzmbbtm16+OGHNW7cOF133XVeL3/w4BGvl/G1xo0jVFBQVGPnB0KGmj4/EDL4e34gZPD3/EDIUNPnB0IGf8+/UNWduaoC5fU9ODExMcrOzpYk5eXlKSoqyuuwHTt26MEHH9TMmTPVqVOn84wKAADwy3jdFdO9e3fl5OQoPj5exhilpqYqPT1dkZGR6tat2xmvM3PmTLlcLj3xxBOSju8FWrBgwcVNDgAAUAWvBSc4OPi0T0G1aNHitMtlZWV5/k+ZAQAA/sSB/gAAgHUoOAAAwDoUHAAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAQAA1qHgAAAA61BwAACAdSg4AADAOhQcAABgHQoOAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1KDgAAMA6FBwAAGAdCg4AALAOBQcAAFiHggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOAAAwDoUHAAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAQAA1qHgAAAA61BwAACAdSg4AADAOhQcAABgHQoOAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1KDgAAMA6FBwAAGAdh78D1BTD07J8MmfxhK4+mQMAQCBjDw4AALCO14LjdruVlJSkwYMHKzExUbt27TrtMoWFherZs6dKS0slSceOHdMDDzyghIQEjRgxQoWFhRc/OQAAQBW8Fpy1a9fK5XIpMzNTY8aMUVpaWqXlH330kYYPH66CggLPeUuXLlVUVJReffVV9e/fX/Pnz7/4yQEAAKrg9T04ubm5iouLkyS1bt1a+fn5lZYHBwcrPT1dt956a6Xr3HPPPZKkG2644ZwKTsOGdeRwhJxXeF9o3DjC3xHOS3Xk9fc2qOnzAyGDv+cHQgZ/zw+EDDV9fiBk8Pf8C+GvzF4LTnFxsZxOp+d0SEiIysvL5XAcv2psbOwZrxMRcXyF6tatq6KiIq9BDh48cs6hfaVx4wgVFHjPHkgudl5/b4OaPj8QMvh7fiBk8Pf8QMhQ0+cHQgZ/z79Q1Z25qgLl9SUqp9OpkpISz2m32+0pN+dynZKSEtWrV+98sgIAAPwiXgtOTEyMsrOzJUl5eXmKioryeqMxMTH68MMPJUnZ2dlq27btL4wJAABw7ry+RNW9e3fl5OQoPj5exhilpqYqPT1dkZGR6tat2xmvM2TIEI0fP15DhgxRaGioZs6cedGDAwAAVMVrwQkODlZKSkql81q0aHHa5bKy/nsgu9q1a+uZZ565CPEAAADOHwf6AwAA1qHgAAAA61BwAACAdSg4AADAOhQcAABgHQoOAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1KDgAAMA6FBwAAGAdCg4AALAOBQcAAFiHggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOAAAwDoUHAAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAQAA1qHgAAAA61BwAACAdSg4AADAOhQcAABgHQoOAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1KDgAAMA6FBwAAGAdCg4AALAOBQcAAFjH4e8A8J3haVnVPmPxhK7VPgMAAG/YgwMAAKxDwQEAANah4AAAAOtQcAAAgHW8vsnY7XYrOTlZ27ZtU1hYmKZNm6amTZt6li9btkwZGRlyOBwaOXKkunTpou+//17jxo2TMUb169fXzJkzVbt27WpdEQAAgBO87sFZu3atXC6XMjMzNWbMGKWlpXmWFRQUaMmSJcrIyNCiRYs0a9YsuVwuvfjii+rdu7deeeUVtWzZUsuXL6/WlQAAADiZ14KTm5uruLg4SVLr1q2Vn5/vWbZ582a1adNGYWFhioiIUGRkpLZu3aqrrrpKhw8fliQVFxfL4eDT6AAAwHe8No/i4mI5nU7P6ZCQEJWXl8vhcKi4uFgRERGeZXXr1lVxcbF+97vfaebMmXr77bflcrl0//33ew3SsGEdORwhF7ga1adx4wjvFwog/s5bHfNtXKdfWwZ/zw+EDP6eHwgZavr8QMjg7/kXwl+ZvRYcp9OpkpISz2m32+3ZI3PqspKSEkVERCgpKUlPPvmk4uLi9MEHH2j8+PF6/vnnzzrn4MEjF7oO1aZx4wgVFBT5O8Z58Xfeiz3f3/eBv+cHQgZ/zw+EDP6eHwgZavr8QMjg7/kXqrozV1WgvL5EFRMTo+zsbElSXl6eoqKiPMuio6OVm5ur0tJSFRUVaefOnYqKilK9evU8e3aaNGniebkKAADAF7zuwenevbtycnIUHx8vY4xSU1OVnp6uyMhIdevWTYmJiUpISJAxRqNHj1Z4eLgmT56slJQUud1uGWOUlJTki3UBAACQdA4FJzg4WCkpKZXOa9Gihef/gwYN0qBBgyotv/zyy/Xyyy9fpIgAAADnhwP9AQAA61BwAACAdSg4AADAOhQcAABgHQoOAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1KDgAAMA6Xr+LCrDF8LQsn8xZPKGrT+YAAKrGHhwAAGAdCg4AALAOBQcAAFiHggMAAKzDm4zhM7zJFwDgK+zBAQAA1qHgAAAA61BwAACAdSg4AADAOhQcAABgHQoOAACwDgUHAABYh4IDAACsQ8EBAADW4UjGgA/5+2jO/p4PAL7CHhwAAGAdCg4AALAOBQcAAFiHggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOAAAwDoc6A9AjcLBDoGagT04AADAOhQcAABgHQoOAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1ONAfAJ/iQHsAfMFrwXG73UpOTta2bdsUFhamadOmqWnTpp7ly5YtU0ZGhhwOh0aOHKkuXbroyJEjSk5O1p49e1RWVqbJkycrOjq6WlcEAH4tfFHyKHio6bwWnLVr18rlcikzM1N5eXlKS0vTggULJEkFBQVasmSJXnvtNZWWliohIUGxsbFatGiRWrZsqaeeekpbt27V1q1bKTgAAMBnvBac3NxcxcXFSZJat26t/Px8z7LNmzerTZs2CgsLU1hYmCIjI7V161Z9/PHH6t27t+6++27VrVtXU6ZM8RqkYcM6cjhCfsGqVI/GjSP8HeG8+Duvv+cHQgZ/zw+EDP6eHwgZbJxv4zr92jL4e/6F8FdmrwWnuLhYTqfTczokJETl5eVyOBwqLi5WRMR/g9etW1fFxcU6ePCgDh8+rEWLFumNN97Q9OnT9dRTT511zsGDR37BalSPxo0jVFBQ5O8Y58Xfef09PxAy+Ht+IGTw9/xAyGDb/Iv5+/DX+j4sfz8n+Hv+haruzFUVKK+fonI6nSopKfGcdrvdcjgcZ1xWUlKiiIgINWjQQF27Hn9gdenSpdJeHwAAgOrmteDExMQoOztbkpSXl6eoqCjPsujoaOXm5qq0tFRFRUXauXOnoqKi1LZtW3344YeSpI0bN+ryyy+vpvgAAACn8/oSVffu3ZWTk6P4+HgZY5Samqr09HRFRkaqW7duSkxMVEJCgowxGj16tMLDw3Xvvffqscce0+DBg+VwODR9+nRfrAsAAICkcyg4wcHBSklJqXReixYtPP8fNGiQBg0aVGl5gwYN9Oyzz16kiAAAAOeHIxkDAADrUHAAAIB1KDgAAMA6FBwAAGAdCg4AALAOBQcAAFiHggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOAAAwDoUHAAAYB0KDgAAsI7XbxMHANhleFqWT+YsntDVJ3OAM2EPDgAAsA4FBwAAWIeCAwAArEPBAQAA1qHgAAAA61BwAACAdSg4AADAOhQcAABgHQoOAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1KDgAAMA6FBwAAGAdCg4AALAOBQcAAFiHggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOAAAwDoUHAAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAQAA1nH4OwAAADXN8LQsn8xZPKGrT+YEIvbgAAAA63gtOG63W0lJSRo8eLASExO1a9euSsuXLVumAQMGaNCgQVq3bl2lZf/617/UqVOni5sYAADAC68vUa1du1Yul0uZmZnKy8tTWlqaFixYIEkqKCjQkiVL9Nprr6m0tFQJCQmKjY1VWFiY9u3bp/T0dJWXl1f7SgAAAJzM6x6c3NxcxcXFSZJat26t/Px8z7LNmzerTZs2CgsLU0REhCIjI7V161aVlpZqypQpSk5OrrbgAAAAVfG6B6e4uFhOp9NzOiQkROXl5XI4HCouLlZERIRnWd26dVVcXKyUlBQNHz5cl1xyyTkHadiwjhyOkPOMX/0aN47wfqEA4u+8/p4fCBn8PT8QMvh7fiBkqOnzAyFDdcz39zqdr0DI668MXguO0+lUSUmJ57Tb7ZbD4TjjspKSEoWGhuqzzz7T7t279dxzz+nQoUMaPXq0Zs+efdY5Bw8eudB1qDaNG0eooKDI3zHOi7/z+nt+IGTw9/xAyODv+YGQoabPD4QMF3s+zwmBmaGqAuW14MTExGjdunXq06eP8vLyFBUV5VkWHR2tOXPmqLS0VC6XSzt37lR0dLRWr17tuUxsbKzXcgMAAHAxeS043bt3V05OjuLj42WMUWpqqtLT0xUZGalu3bopMTFRCQkJMsZo9OjRCg8P90VuAACAKnktOMHBwUpJSal0XosWLTz/HzRokAYNGlTl9XNycn5BPAAAgPPHgf4AAIB1KDgAAMA6FBwAAGAdCg4AALAOBQcAAFiHggMAAKxDwQEAANah4AAAAOt4PdCfLYanZflkzuIJXX0yBwAAVI09OAAAwDoUHAAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAQAA1qHgAAAA61BwAACAdSg4AADAOjXmSMYAAJzA0e3txx4cAABgHQoOAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1KDgAAMA6FBwAAGAdCg4AALAOBQcAAFiHggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOAAAwDoUHAAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAQAA1qHgAAAA61BwAACAdSg4AADAOhQcAABgHQoOAACwjsPbBdxut5KTk7Vt2zaFhYVp2rRpatq0qWf5smXLlJGRIYfDoZEjR6pLly76/vvvNWnSJFVUVMgYo5SUFDVv3rxaVwQAAOAEr3tw1q5dK5fLpczMTI0ZM0ZpaWmeZQUFBVqyZIkyMjK0aNEizZo1Sy6XS3PnztXtt9+uJUuW6N5779WsWbOqdSUAAABO5nUPTm5uruLi4iRJrVu3Vn5+vmfZ5s2b1aZNG4WFhSksLEyRkZHaunWrxo8fr4iICElSRUWFwsPDvQZp2LCOHI6QC12PgNG4cQTz/czfGfw9PxAy+Ht+IGSo6fMDIYO/5wdCBn/P92cGrwWnuLhYTqfTczokJETl5eVyOBwqLi72FBlJqlu3roqLi9WoUSNJ0tdff63p06frueee8xrk4MEjF5I/4BQUFDHfz/ydwd/zAyGDv+cHQoaaPj8QMvh7fiBk8Pd8X2SoqkB5fYnK6XSqpKTEc9rtdsvhcJxxWUlJiafwrF+/XqNGjdJTTz3F+28AAIBPeS04MTExys7OliTl5eUpKirKsyw6Olq5ubkqLS1VUVGRdu7cqaioKK1fv15PPPGEXnjhBf35z3+uvvQAAABn4PUlqu7duysnJ0fx8fEyxig1NVXp6emKjIxUt27dlJiYqISEBBljNHr0aIWHhys1NVVlZWWaMGGCJKlZs2ZKSUmp9pUBAACQzqHgBAcHn1ZOWrRo4fn/oEGDNGjQoErL33rrrYsUDwAA4PxxoD8AAGAdCg4AALAOBQcAAFiHggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOAAAwDoUHAAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAQAA1qHgAAAA61BwAACAdSg4AADAOhQcAABgHQoOAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1KDgAAMA6FBwAAGAdCg4AALAOBQcAAFiHggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOAAAwDoUHAAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAQAA1qHgAAAA61BwAACAdSg4AADAOhQcAABgHQoOAACwDgUHAABYh4IDAACs4/B2AbfbreTkZG3btk1hYWGaNm2amjZt6lm+bNkyZWRkyOFwaOTIkerSpYsKCwv1yCOP6NixY2rSpImefPJJ1a5du1pXBAAA4ASve3DWrl0rl8ulzMxMjRkzRmlpaZ5lBQUFWrJkiTIyMrRo0SLNmjVLLpdL8+fPV9++ffXqq6+qVatWyszMrNaVAAAAOJnXgpObm6u4uDhJUuvWrZWfn+9ZtnnzZrVp00ZhYWGKiIhQZGSktm7dWuk6N9xwgz755JNqig8AAHC6IGOMOdsFHn30UfXo0UOdOnWSJHXu3Flr166Vw+HQm2++qe3bt2vs2LGSpHHjxql///6aMmWKVq5cqVq1aum7777TuHHjtHTp0upfGwAAAJ3DHhyn06mSkhLPabfbLYfDccZlJSUlioiIqHR+SUmJ6tWrd7FzAwAAVMlrwYmJiVF2drYkKS8vT1FRUZ5l0dHRys3NVWlpqYqKirRz505FRUUpJiZGH374oSQpOztbbdu2rab4AAAAp/P6EtWJT1Ft375dxhilpqYqOztbkZGR6tatm5YtW6bMzEwZY3TvvfeqZ8+eOnDggMaPH6+SkhI1bNhQM2fOVJ06dXy1TgAAoIbzWnAAAAB+bTjQHwAAsA4FBwAAWIeCAwAArOP1qxpqGm9fTeErmzZt0owZM7RkyRKfzy4rK9OkSZO0d+9euVwujRw5Ut26dfNphoqKCj322GP65ptvFBQUpMcff7zSJ/h85aefftKAAQO0ePFitWjRwqezb7nlFjmdTknSZZddpieffNKn8yXpf//3f5WVlaWysjINGTJEt912m89mv/7661qxYoUkqbS0VF9++aVycnJ8etiJsrIyTZgwQXv37lVwcLCmTp3q08eBy+XSxIkT9d1338npdCopKUl/+tOffDYf/1VYWKinn37aLz+HkrRv3z5lZWXpT3/6k6688kr95je/8UuOXxMKzilO/mqKvLw8paWlacGCBT7N8I9//ENvvfWW376/66233lKDBg309NNP6+eff1b//v19XnDWrVsnScrIyNCGDRs0e/Zsn98PZWVlSkpKUq1atXw6Vzr+hG6M8UvBPWHDhg364osvtHTpUh09elSLFy/26fwBAwZowIABkqTHH39ct956q8+PqfXhhx+qvLxcGRkZysnJ0Zw5czRv3jyfzV+2bJnq1KmjZcuW6euvv9bUqVO1aNEin83Hf2VnZ3uO0O8PO3fu1LJly1SvXj2NGzeOgnMOeInqFGf7agpfiYyM9Okv0VP16tVLDz74oCTJGKOQkBCfZ/jb3/6mqVOnSpK+//57vxwscvr06YqPj1eTJk18Pnvr1q06evSohg8frjvuuEN5eXk+z/Dxxx8rKipKo0aN0n333afOnTv7PIMkbdmyRTt27NDgwYN9PrtZs2aqqKiQ2+1WcXGx5yCnvrJjxw7dcMMNkqTmzZtr586dPp1/snnz5tXoI9J//PHHfi04rVq1Ut++ffXnP/9ZV1xxhU9nr1q1SomJiZX+bd682acZLgR7cE5RXFzseVlAkkJCQlReXu7TX2w9e/bUnj17fDbvVHXr1pV0fFv8/e9/10MPPeSXHA6HQ+PHj9d7772nZ555xqezX3/9dTVq1EhxcXF6/vnnfTpbkmrVqqW7775bt912m7799luNGDFCq1at8unj8ODBg/r++++1cOFC7dmzRyNHjtSqVasUFBTkswzS8ZfJRo0a5dOZJ9SpU0d79+5V7969dfDgQS1cuNCn86+66iqtW7dOf/vb37Rp0ybt379fFRUVPv2j491339XSpUu1d+9ehYaG6t1339V9992n2NhYn2WYPXu2Pv/8c0nSiy++6PM/usrKynTs2DFFRET4dO7JGjVqpBEjRvhldq9evdSrVy+/zP4lKDinONtXU9Qk+/bt06hRo5SQkKB+/fr5Lcf06dP1yCOPaNCgQXrnnXd8dsDI1157TUFBQfr000/15Zdfavz48VqwYIEaN27sk/nNmjVT06ZNFRQUpGbNmqlBgwYqKCjQ73//e5/Ml6QGDRqoefPmCgsLU/PmzRUeHq7CwkKf7ho/fPiwvvnmG7Vr185nM0/24osvqmPHjhozZoz27dunO++8UytXrlR4eLhP5t96663auXOnEhISFBMTo6uvvtrnT+59+vRRnz59NG/ePP32t7/VkCFDfDpfkkaPHu3zmSf77LPPavQR+VetWqVXXnml0nljx45VdHS0nxKdm5r3zO1FTEyM1q1bpz59+pz21RQ1xYEDBzR8+HAlJSWpffv2fsnwxhtvaP/+/br33ntVu3ZtBQUFKTjYd6+onvzDnJiYqOTkZJ+VG0lavny5tm/fruTkZO3fv1/FxcU+nS9Jbdu21csvv6y77rpLP/74o44ePaoGDRr4NMPGjRv99hiUpHr16ik0NFSSVL9+fZWXl6uiosJn87ds2aL27dtr0qRJ2rJli77//nufzcZ/ffDBB4qPj/d3DL9hD44lunfvrpycHMXHx3u+mqKmWbhwoQ4fPqz58+dr/vz5ko6/8dmXb7bt0aOHJk6cqKFDh6q8vFyTJk3yy5t9/WXgwIGaOHGihgwZoqCgIKWmpvp8T2KXLl20ceNGDRw4UMYYJSUl+XzvwTfffKPLLrvMpzNPNmzYME2aNEkJCQkqKyvT6NGjffq1M02bNtXcuXO1cOFCRURE6IknnvDZ7FM98MADfpvtb99++62aNWvm7xg4T3xVAwAAsA6fogIAANah4AAAAOtQcAAAgHUoOAAAwDoUHAAAYB0KDgAAsA4FBwAAWOf/AxFO+l4hDAMXAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = pyplot.subplots()\n",
    "\n",
    "totals = []\n",
    "for symbol in SYMBOLS:\n",
    "    total = sum(position[symbol] for position in frequencies.values())\n",
    "    totals.append(total)\n",
    "\n",
    "total_sum = sum(totals)\n",
    "totals = [i / total_sum for i in totals]\n",
    "\n",
    "ax.set_title(\"Frequency of occurences of each symbol over all solutions\")\n",
    "ax.bar(SYMBOLS, totals)\n",
    "\n",
    "fig.savefig(\"plots/symbol_frequency.jpg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Probability of each symbol occuring\n",
    "\n",
    "Similar to the last one, although only takes into account whether the symbol occurs *somewhere* in the solution, not how many times it occurs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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moBRnu7g9cAQHJaZHjx46efKkevbsKafTqerVq2vWrFmu6wMDAxUVFaVLly6pX79+atSokWrWrKk1a9aoY8eO8vX1VePGjXX+/HnXD++aNWtq8ODBunDhgho2bFjsQ/6tWrVSXFyccnJy1K1bN7Vq1Urjxo1TdHT0dddv2rSpnnzySQ0YMEBOp1NBQUGaN29eoS9G9PX11bvvvqupU6cqPj5eeXl5GjJkiH73u99JkkaMGKFBgwZJkoKDgzVt2jRVqVKlwOXR0dHq3r27goOD1bJlywLn9uzZU6dOnXIdgahataqmT59e6P6oXLmyZs2apVGjRikvL08BAQF64403FBQUpNmzZ2vGjBnKysqSMUYzZszQ3Xffne/2QUFBeuuttzRlyhRdunRJXl5eev311xUaGlroabwXXnhBcXFx6tatm/Ly8lS3bl2NHj1a/v7+atmypR599FFVqFBBISEhuu+++5SSkqKIiIjr7qMjR44Ueh+v6Nq1q7Zv366OHTuqXLlyuuuuu1xvL/bz81P79u3173//+5qjVMVRo0YNvf322zp69KjuvPNO134fN26cpk6dqi5duignJ0cRERF67rnnbnj7hRk4cKAmTJigZcuWycfHR/Xr19fBgwevWS8qKkqHDx9W165d5e/vr2rVqqlcuXLXrOfn56eOHTtqy5YtatCggSQV+/FQmAEDBmj06NHq3Lmz/Pz8VLt2bXXu3FkOh6PQ5wfp8nPEiBEj9MwzzygoKEgdOnRwXRccHKx69erp0Ucf1cKFC13Li3rewe3Dy3B8DrehXbt2afz48Vq1alW+0x+4vVy8eFH9+vXTxIkTXa/lsc2mTZt09uxZ12vnpk6dqjJlymjEiBEeTgaULE5R4bYzatQoDR8+XBMnTqTc3Ma++OILtWzZUo0aNbK23EiXXwC+fPlyPfbYY+rUqZNSU1Nv+dEkoDTiCA4AALAOR3AAAIB1KDgAAMA6bn8X1Zkzae4eWaRKlfyVmnqRDGQoFRk8PZ8MpSeDp+eTofRk8PT80pLheoKDA6+7nCM4khwOz/9BQDKQobTMJ0PpyeDp+WQoPRk8Pb+0ZLgRFBwAAGAdCg4AALAOBQcAAFiHggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOAAAwDoUHAAAYB0KDgAAsA4FBwAAWIeCAwAArFOsgrN7927FxMRcs3z9+vXq3r27evfurYSEhFseDgAA4GY4ilrhvffe04oVK1SuXLl8y3NycvT6669ryZIlKleunJ544gm1bt1alStXLrGwAAAAxVHkEZyQkBDFx8dfs/zQoUMKCQnRHXfcIT8/PzVs2FA7duwokZAAAAA3osgjOO3bt9exY8euWZ6enq7AwEDX5fLlyys9Pb3IgZUq+cvh8LnBmCUvODiw6JXIQIbbZD4ZSk8GT88nQ+nJcCvndxn+j1u2rcKs/MPjbplzPUUWnIIEBAQoIyPDdTkjIyNf4SlIaurFmx1ZYoKDA3XmTBoZyFAqMnh6PhlKTwZPzydD6cng6fk3yx2ZCyp+N/0uqpo1ayolJUU//fSTsrOz9dVXX+nBBx+86YAAAAC3yg0fwVm5cqUuXryo3r17a/To0Xr66adljFH37t1VpUqVksgIAABwQ4pVcKpVq+Z6G3iXLl1cy1u3bq3WrVuXTDIAAICbxAf9AQAA61BwAACAdSg4AADAOhQcAABgHQoOAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1KDgAAMA6FBwAAGAdCg4AALAOBQcAAFiHggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOAAAwDoUHAAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAQAA1qHgAAAA61BwAACAdSg4AADAOhQcAABgHQoOAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1KDgAAMA6FBwAAGAdCg4AALAOBQcAAFiHggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOAAAwDoUHAAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAQAA1qHgAAAA61BwAACAdSg4AADAOhQcAABgHQoOAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1iiw4TqdTEyZMUO/evRUTE6OUlJR817///vuKiopS9+7dtXbt2hILCgAAUFyOolZITExUdna2Fi9erOTkZE2fPl1z5syRJF24cEEffvih1qxZo8zMTHXt2lWRkZElHhoAAKAwRRacnTt3KiIiQpIUFhamffv2ua4rV66c7rrrLmVmZiozM1NeXl5FDqxUyV8Oh88viFwygoMDPR2BDGQoNfPJUHoyeHo+GUpPBk/PvxmezFxkwUlPT1dAQIDrso+Pj3Jzc+VwXL5p1apV1alTJ+Xl5Wnw4MFFDkxNvfgL4paM4OBAnTmTRgYylIoMnp5PhtKTwdPzyVB6Mnh6/s1yR+aCSlSRr8EJCAhQRkaG67LT6XSVm6SkJJ0+fVrr1q3Txo0blZiYqD179tyiyAAAADenyIITHh6upKQkSVJycrJq1arluu6OO+5Q2bJl5efnpzJlyigwMFAXLlwoubQAAADFUOQpqsjISG3evFnR0dEyxmjatGmaP3++QkJC1KZNG23ZskW9evWSt7e3wsPD1bRpU3fkBgAAKFCRBcfb21uxsbH5ltWsWdP1/6FDh2ro0KG3PhkAAMBN4oP+AACAdSg4AADAOhQcAABgHQoOAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1KDgAAMA6FBwAAGAdCg4AALAOBQcAAFiHggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOAAAwDoUHAAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAQAA1qHgAAAA61BwAACAdSg4AADAOhQcAABgHQoOAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1KDgAAMA6FBwAAGAdCg4AALAOBQcAAFiHggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOAAAwDoUHAAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAQAA1qHgAAAA61BwAACAdSg4AADAOhQcAABgHQoOAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1HEWt4HQ6NWnSJB04cEB+fn6aOnWqqlev7rr+888/1zvvvCNjjOrXr6+JEyfKy8urREMDAAAUpsiCk5iYqOzsbC1evFjJycmaPn265syZI0lKT0/XzJkz9eGHHyooKEjvvfeeUlNTFRQUVOLBS7OB09e7Zc77o1u7ZQ4AAP9tijxFtXPnTkVEREiSwsLCtG/fPtd1X3/9tWrVqqW4uDj16dNHlStXvu3LDQAA8Lwij+Ckp6crICDAddnHx0e5ublyOBxKTU3Vtm3btHz5cvn7+6tv374KCwtTaGhogdurVMlfDofPrUl/CwUHB3o6wg0ricylYT+QwfPzyVB6Mnh6PhlKTwZPz78ZnsxcZMEJCAhQRkaG67LT6ZTDcflmFStW1G9/+1sFBwdLkh566CHt37+/0IKTmnrxl2a+5YKDA3XmTJqnY9ywW525NOwHMnh+PhlKTwZPzydD6cng6fk3yx2ZCypRRZ6iCg8PV1JSkiQpOTlZtWrVcl1Xv359HTx4UOfOnVNubq52796t++677xZFBgAAuDlFHsGJjIzU5s2bFR0dLWOMpk2bpvnz5yskJERt2rTR8OHDNWjQIElShw4d8hUgAAAATyiy4Hh7eys2Njbfspo1a7r+36lTJ3Xq1OnWJwMAALhJfNAfAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1KDgAAMA6FBwAAGAdCg4AALAOBQcAAFiHggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOAAAwDoUHAAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAQAA1nF4OgBKxsDp690y5/3Rrd0yBwCAG8ERHAAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAQAA1qHgAAAA61BwAACAdSg4AADAOhQcAABgHQoOAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1KDgAAMA6Dk8HAErKwOnr3Tbr/dGt3TYLAFA0juAAAADrUHAAAIB1OEWFEuOuU0ScHgIA/BxHcAAAgHUoOAAAwDoUHAAAYB1egwNYjtdCAbgdcQQHAABYh4IDAACswykqAIDbcMoU7sIRHAAAYB0KDgAAsA6nqIASxOF4APAMCg6A2wJlE7i9cIoKAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1eBcVgBLHO5gAuFuRR3CcTqcmTJig3r17KyYmRikpKdddZ9CgQVq4cGGJhAQAALgRRR7BSUxMVHZ2thYvXqzk5GRNnz5dc+bMybfOm2++qQsXLpRYSAD4b8dRLMC9ijyCs3PnTkVEREiSwsLCtG/fvnzXr169Wl5eXq51AAAAPK3IIzjp6ekKCAhwXfbx8VFubq4cDocOHjyoVatWafbs2XrnnXeKNbBSJX85HD43n7iEBAcHejrCDSsNmclQOjJ4ej4ZSk+Gkpjv6ft0M2zcD56efzM8mbnIghMQEKCMjAzXZafTKYfj8s2WL1+uU6dOacCAATp+/Lh8fX119913q3nz5gVuLzX14i2IfWsFBwfqzJk0T8e4YaUhMxlKRwZPzydD6clwq+fz/HiZp/eDp+ffLHdkLqhEFVlwwsPDtWHDBnXs2FHJycmqVauW67qRI0e6/h8fH6/KlSsXWm4AAADcociCExkZqc2bNys6OlrGGE2bNk3z589XSEiI2rRp446MAAAAN6TIguPt7a3Y2Nh8y2rWrHnNei+++OKtSwUAuOV4JxduJ3ySMQAAsA4FBwAAWIeCAwAArEPBAQAA1qHgAAAA61BwAACAdSg4AADAOhQcAABgHQoOAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1KDgAAMA6FBwAAGAdCg4AALAOBQcAAFiHggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOAAAwDoOTwcAAOB2MnD6erfNen90a7fNKm04ggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOAAAwDoUHAAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAQAA1qHgAAAA61BwAACAdSg4AADAOhQcAABgHQoOAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrODwd4FYbOH2922a9P7q122YBAIDi4wgOAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1KDgAAMA61n0ODgAAhXHX56XxWWmexREcAABgHQoOAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrFPk2cafTqUmTJunAgQPy8/PT1KlTVb16ddf1H3zwgT7++GNJUosWLfQ///M/JZcWAACgGIo8gpOYmKjs7GwtXrxYw4cP1/Tp013XHT16VCtWrNCiRYuUkJCgTZs26bvvvivRwAAAAEUp8gjOzp07FRERIUkKCwvTvn37XNf9+te/1p///Gf5+PhIknJzc1WmTJlCt1epkr8cDp9fkrnUCA4OvK3nk6H0ZPD0fDKUngyenk8GMpSW+UUWnPT0dAUEBLgu+/j4KDc3Vw6HQ76+vgoKCpIxRjNmzFC9evUUGhpa6PZSUy/+8tSlxJkzabf1fDKUngyenk+G0pPB0/PJQAZ3zy+oRBV5iiogIEAZGRmuy06nUw7Hf3pRVlaWfv/73ysjI0MTJ068BVEBAAB+mSILTnh4uJKSkiRJycnJqlWrlus6Y4xeeOEF1a5dW7Gxsa5TVQAAAJ5U5CmqyMhIbd68WdHR0TLGaNq0aZo/f75CQkLkdDq1fft2ZWdn64svvpAkvfLKK3rwwQdLPDgAAEBBiiw43t7eio2NzbesZs2arv/v3bv31qcCAAD4BfigPwAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAQAA1qHgAAAA61BwAACAdSg4AADAOhQcAABgHQoOAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1KDgAAMA6FBwAAGAdCg4AALAOBQcAAFiHggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOAAAwDoUHAAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAQAA1qHgAAAA61BwAACAdSg4AADAOhQcAABgHQoOAACwDgUHAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1KDgAAMA6FBwAAGAdCg4AALAOBQcAAFiHggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOAAAwDoUHAAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAQAA1qHgAAAA61BwAACAdSg4AADAOhQcAABgnSILjtPp1IQJE9S7d2/FxMQoJSUl3/UJCQmKiopSr169tGHDhhILCgAAUFyOolZITExUdna2Fi9erOTkZE2fPl1z5syRJJ05c0YLFizQ0qVLlZWVpT59+qhp06by8/Mr8eAAAAAFKfIIzs6dOxURESFJCgsL0759+1zX7dmzRw8++KD8/PwUGBiokJAQfffddyWXFgAAoBi8jDGmsBVeffVVtWvXTi1atJAktWzZUomJiXI4HPrHP/6hgwcPasSIEZKkkSNHqmvXrmrSpEnJJwcAAChAkUdwAgIClJGR4brsdDrlcDiue11GRoYCAwNLICYAAEDxFVlwwsPDlZSUJElKTk5WrVq1XNc1aNBAO3fuVFZWltLS0nTo0KF81wMAAHhCkaeonE6nJk2apIMHD8oYo2nTpikpKUkhISFq06aNEhIStHjxYhljNHjwYLVv395d2QEAAK6ryIIDAADw34YP+gMAANah4AAAAOtQcAAAgHWK/CRjm115AfWBAwfk5+enqVOnqnr16h7Jsnv3bs2aNUsLFixw69ycnByNHTtWx48fV3Z2tp5//nm1adPGrRny8vI0btw4HT58WF5eXpo8ebLH3o139uxZRUVF6f3331fNmjXdPr9bt24KCAiQJFWrVk2vv/662zPMmzdP69evV05Ojp544gn17NnTrfOXLVumjz76SJKUlZWl/fv3a/PmzapQoYJb5ufk5Gj06NE6fvy4vL29NWXKFLc/FrKzszVmzBgdPXpUAQEBmjBhgu699163ZsB/nDt3TjNnzvTI96MknTx5UuvXr9e9996rOnXq6M477/RIjv82t3XBKezPULjTe++9pxUrVqhcuXJun71ixQpVrFhRM2fO1E8//aSuXbu6veBc+RtmixYt0rZt2/TGG2945OuQk5OjCRMmqGzZsm6fLV3+YW6McXvJvdq2bdv09ddfa+HChcrMzNT777/v9gxRUVGKioqSJE2ePFndu3d3W7mRpM8//1y5ublatGiRNm/erDfffFPx8fFumy9d/ht//v7+SkhI0D//+U9NmTJFf/nLX9yaAf+RlJTk+kR/Tzh06JASEhJUoUIFjRw5koJTTLf1KarC/gyFO4WEhLj9CfSKDh066KWXXpIkGWPk4+Pj9gxt27bVlClTJEknTpxw6w+zq8XFxSk6Olq/+tWvPDL/u+++U2ZmpgYOHKj+/fsrOTnZ7Rk2bdqkWrVqaciQIXruuefUsmVLt2e4Yu/evfrhhx/Uu3dvt84NDQ1VXl6enE6n0tPTXR9s6k4//PCDmjdvLkmqUaOGDh065PYMV8THx2vhwoUem18abNq0yaMFp169eurcubN++9vfqnbt2m6fv3r1asXExOT7t2fPHrfnuFG39RGc9PR01+kASfLx8VFubq7bn9Dat2+vY8eOuXXmFeXLl5d0eV8MHTpUw4YN80gOh8OhUaNGae3atZo9e7bb5y9btkxBQUGKiIjQn/70J7fPl6SyZcvq6aefVs+ePXXkyBE988wzWr16tVsfj6mpqTpx4oTmzp2rY8eO6fnnn9fq1avl5eXltgxXzJs3T0OGDHH7XH9/fx0/flyPPvqoUlNTNXfuXLdnqFu3rjZs2KC2bdtq9+7dOnXqlPLy8tz6C8gnn3yihQsX6vjx4/L19dUnn3yi5557Tk2bNnVbBkl64403tGvXLknSBx984PZfwnJycnTp0iWPfkp/UFCQnnnmGY/N79Chgzp06OCx+Tfrti44hf0ZitvJyZMnNWTIEPXp00ddunTxWI64uDj9/ve/V69evfTxxx/L39/fbbOXLl0qLy8vbd26Vfv379eoUaM0Z84cBQcHuy1DaGioqlevLi8vL4WGhqpixYo6c+aMqlat6rYMFStWVI0aNeTn56caNWqoTJkyOnfunNsPiV+4cEGHDx/W7373O7fOlS7/EG3WrJmGDx+ukydPasCAAVq5cqXKlCnjtgzdu3fXoUOH1KdPH4WHh6t+/fpu/8HesWNHdezYUfHx8apcubKeeOIJt86/4uWXX/bI3Cu++uorNWzY0KMZPG316tX661//mm/ZiBEj1KBBAw8lKp7b76f5VcLDw7VhwwZ17Njxmj9Dcbv497//rYEDB2rChAlq3LixRzIsX75cp06d0uDBg1WuXDl5eXnJ29u9Z0+v/uaNiYnRpEmT3FpuJGnJkiU6ePCgJk2apFOnTik9Pd3tGRo2bKgPP/xQTz31lE6fPq3MzExVrFjRrRkkaceOHR57PFaoUEG+vr6SpDvuuEO5ubnKy8tza4a9e/eqcePGGjt2rPbu3asTJ064dT7+Y+PGjYqOjvZ0DI/iCM5/ocjISG3evFnR0dGuP0Nxu5k7d64uXLigd999V++++66kyy96ducLbdu1a6cxY8aob9++ys3N1dixYz32Ql9P6tGjh8aMGaMnnnhCXl5emjZtmtuPKLZq1Uo7duxQjx49ZIzRhAkTPPK6rMOHD6tatWpunytJTz75pMaOHas+ffooJydHL7/8sluPJkpS9erV9dZbb2nu3LkKDAzUa6+95tb5V3vxxRc9Nrs0OHLkiEJDQz0dAzeBP9UAAACsc1u/iwoAANiJggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOAAAwDoUHAAAYJ3/B8zM6Or26fNCAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = pyplot.subplots()\n",
    "\n",
    "totals = []\n",
    "for symbol in SYMBOLS:\n",
    "    totals.append(sum(symbol in line for line in data) / len(data))\n",
    "\n",
    "ax.set_title(\"Probability of occurence of each symbol in a given solution\")\n",
    "ax.bar(SYMBOLS, totals)\n",
    "\n",
    "fig.savefig(\"plots/symbol_probability.jpg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Frequency of occurence of each symbol in a given position"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1080x1440 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = pyplot.subplots(nrows=4, ncols=2)\n",
    "ax = ax.flatten()\n",
    "\n",
    "fig.set_figheight(20)\n",
    "fig.set_figwidth(15)\n",
    "\n",
    "for n, position in enumerate(POSITIONS):\n",
    "    totals = []\n",
    "    for symbol in SYMBOLS:\n",
    "        totals.append(frequencies[int(position)][symbol])\n",
    "\n",
    "    totals = [i / len(data) for i in totals]\n",
    "\n",
    "    ax[n].set_title(f\"Frequency of occurence of symbols in position {position}\")\n",
    "    ax[n].bar(SYMBOLS, totals)\n",
    "\n",
    "fig.savefig(\"plots/frequency_of_symbols_per_position.jpg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Probability of occuring in a given position per symbol\n",
    "\n",
    "This shows, for each symbol, the probability that it will be in a given position in the answer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1440x2160 with 15 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = pyplot.subplots(nrows=5, ncols=3)\n",
    "ax = ax.flatten()\n",
    "\n",
    "fig.set_figheight(30)\n",
    "fig.set_figwidth(20)\n",
    "for n, symbol in enumerate(SYMBOLS):\n",
    "    totals = []\n",
    "    for position in POSITIONS:\n",
    "        totals.append(frequencies[int(position)][symbol])\n",
    "\n",
    "    total_sum = sum(totals)\n",
    "    totals = [i / total_sum for i in totals]\n",
    "\n",
    "    ax[n].set_title(f\"Frequency of occurences, per position, of '{symbol}'\")\n",
    "    ax[n].bar(POSITIONS, totals)\n",
    "\n",
    "fig.savefig(\"plots/frequency_of_positions_per_symbol.jpg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Permutations of operators by frequency\n",
    "\n",
    "This shows the probability that a result will be made up of operators in a given order. For example `+` would be any answers involving just a `+` such as `12+34=46`. There are 20 possibilites"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " 1) +: 18.79%\n",
      " 2) -: 18.79%\n",
      " 3) /:  6.93%\n",
      " 4) *:  6.93%\n",
      " 5) *-:  5.86%\n",
      " 6) -*:  4.01%\n",
      " 7) --:  3.89%\n",
      " 8) /-:  3.83%\n",
      " 9) *+:  3.68%\n",
      "10) +*:  3.68%\n",
      "11) ++:  3.64%\n",
      "12) +-:  2.96%\n",
      "13) -+:  2.96%\n",
      "14) */:  2.60%\n",
      "15) /*:  2.60%\n",
      "16) **:  2.11%\n",
      "17) //:  2.11%\n",
      "18) -/:  1.77%\n",
      "19) +/:  1.44%\n",
      "20) /+:  1.44%\n"
     ]
    }
   ],
   "source": [
    "operator_orders = Counter()\n",
    "\n",
    "for line in data:\n",
    "    order = ''.join(i for i in line if i not in \"0123456789\").rstrip(\"=\")\n",
    "    operator_orders[order] += 1 / len(data)\n",
    "\n",
    "for pos, (form, prob) in enumerate(operator_orders.most_common(), 1):\n",
    "    print(f'{pos:>2}) {form}: {prob*100:5.2f}%')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Most Frequent Answer Formats\n",
    "\n",
    "Similar to the last one, although more interesting as it takes into account the number of digits between operators too. There are 44 possibilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " 1) xx+xx=xx: 18.28%\n",
      " 2) xx-xx=xx: 18.28%\n",
      " 3) xx-x*x=x:  4.01%\n",
      " 4) xx-x-x=x:  3.89%\n",
      " 5) xx/x-x=x:  3.83%\n",
      " 6) x*x+x=xx:  3.68%\n",
      " 7) x+x*x=xx:  3.68%\n",
      " 8) x+x+x=xx:  3.64%\n",
      " 9) xxx/xx=x:  3.46%\n",
      "10) xxx/x=xx:  3.46%\n",
      "11) xx*x=xxx:  3.46%\n",
      "12) x*xx=xxx:  3.46%\n",
      "13) x*x-xx=x:  2.84%\n",
      "14) x*x-x=xx:  2.51%\n",
      "15) x*x*x=xx:  2.11%\n",
      "16) xx/x/x=x:  2.11%\n",
      "17) x-xx/x=x:  1.38%\n",
      "18) x+xx/x=x:  1.05%\n",
      "19) xx/x+x=x:  1.05%\n",
      "20) x+x-xx=x:  0.93%\n",
      "21) x-xx+x=x:  0.93%\n",
      "22) x+xx-x=x:  0.68%\n",
      "23) x-x+xx=x:  0.68%\n",
      "24) xx+x-x=x:  0.68%\n",
      "25) xx-x+x=x:  0.68%\n",
      "26) x+x-x=xx:  0.68%\n",
      "27) x-x+x=xx:  0.68%\n",
      "28) x*xx/x=x:  0.65%\n",
      "29) x/x*xx=x:  0.65%\n",
      "30) xx*x/x=x:  0.65%\n",
      "31) xx/x*x=x:  0.65%\n",
      "32) x*x/xx=x:  0.65%\n",
      "33) x*x/x=xx:  0.65%\n",
      "34) x/x*x=xx:  0.65%\n",
      "35) x/xx*x=x:  0.65%\n",
      "36) x+x/x=xx:  0.39%\n",
      "37) x/x+x=xx:  0.39%\n",
      "38) xx-x/x=x:  0.39%\n",
      "39) x*xx-x=x:  0.25%\n",
      "40) x+xx=xxx:  0.25%\n",
      "41) xx*x-x=x:  0.25%\n",
      "42) xxx-x=xx:  0.25%\n",
      "43) xxx-xx=x:  0.25%\n",
      "44) xx+x=xxx:  0.25%\n"
     ]
    }
   ],
   "source": [
    "operator_orders = Counter()\n",
    "\n",
    "for line in data:\n",
    "    order = ''.join(\"x\" if i in \"0123456789\" else i for i in line)\n",
    "    operator_orders[order] += 1 / len(data)\n",
    "\n",
    "\n",
    "for pos, (form, prob) in enumerate(operator_orders.most_common(), 1):\n",
    "    print(f'{pos:>2}) {form}: {prob*100:5.2f}%')"
   ]
  }
 ],
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