honeycomb_puzzle.ipynb

   1 {
   2  "cells": [
   3   {
   4    "cell_type": "markdown",
   5    "id": "951180ec",
   6    "metadata": {},
   7    "source": [
   8     "# Honeycomb letter puzzle\n",
   9     "Solving the puzzle as posted on [FiveThirtyEight](https://fivethirtyeight.com/features/can-you-solve-the-vexing-vexillology/), also solved by [David Robinson](http://varianceexplained.org/r/honeycomb-puzzle/).\n"
  10    ]
  11   },
  12   {
  13    "cell_type": "code",
  14    "execution_count": 1,
  15    "id": "6f6fa3e7",
  16    "metadata": {},
  17    "outputs": [],
  18    "source": [
  19     "import string\n",
  20     "import collections\n",
  21     "from dataclasses import dataclass\n",
  22     "import itertools"
  23    ]
  24   },
  25   {
  26    "cell_type": "code",
  27    "execution_count": 2,
  28    "id": "7f00bc22",
  29    "metadata": {},
  30    "outputs": [],
  31    "source": [
  32     "def only_letters(text):\n",
  33     "    return ''.join([c.lower() for c in text if c in string.ascii_letters])"
  34    ]
  35   },
  36   {
  37    "cell_type": "code",
  38    "execution_count": 3,
  39    "id": "cb0b4230",
  40    "metadata": {},
  41    "outputs": [
  42     {
  43      "data": {
  44       "text/plain": [
  45        "'hello'"
  46       ]
  47      },
  48      "execution_count": 3,
  49      "metadata": {},
  50      "output_type": "execute_result"
  51     }
  52    ],
  53    "source": [
  54     "only_letters('Hell!o')"
  55    ]
  56   },
  57   {
  58    "cell_type": "code",
  59    "execution_count": 4,
  60    "id": "9546868c",
  61    "metadata": {},
  62    "outputs": [
  63     {
  64      "data": {
  65       "text/plain": [
  66        "101924"
  67       ]
  68      },
  69      "execution_count": 4,
  70      "metadata": {},
  71      "output_type": "execute_result"
  72     }
  73    ],
  74    "source": [
  75     "with open('/usr/share/dict/british-english') as f:\n",
  76     "    words = [line.rstrip() for line in f]\n",
  77     "len(words)"
  78    ]
  79   },
  80   {
  81    "cell_type": "code",
  82    "execution_count": 79,
  83    "id": "88f00e4c",
  84    "metadata": {},
  85    "outputs": [
  86     {
  87      "data": {
  88       "text/plain": [
  89        "172820"
  90       ]
  91      },
  92      "execution_count": 79,
  93      "metadata": {},
  94      "output_type": "execute_result"
  95     }
  96    ],
  97    "source": [
  98     "with open('enable1.txt') as f:\n",
  99     "    words = [line.rstrip() for line in f]\n",
 100     "len(words)"
 101    ]
 102   },
 103   {
 104    "cell_type": "code",
 105    "execution_count": 80,
 106    "id": "1e75fba2",
 107    "metadata": {},
 108    "outputs": [],
 109    "source": [
 110     "words = set(only_letters(w) \n",
 111     "            for w in words \n",
 112     "            if len(only_letters(w)) >= 4\n",
 113     "            if len(frozenset(only_letters(w))) <= 7\n",
 114     "            if 's' not in w)"
 115    ]
 116   },
 117   {
 118    "cell_type": "code",
 119    "execution_count": 81,
 120    "id": "49473123",
 121    "metadata": {},
 122    "outputs": [
 123     {
 124      "data": {
 125       "text/plain": [
 126        "44585"
 127       ]
 128      },
 129      "execution_count": 81,
 130      "metadata": {},
 131      "output_type": "execute_result"
 132     }
 133    ],
 134    "source": [
 135     "len(words)"
 136    ]
 137   },
 138   {
 139    "cell_type": "code",
 140    "execution_count": 82,
 141    "id": "e1f9b35e",
 142    "metadata": {},
 143    "outputs": [
 144     {
 145      "data": {
 146       "text/plain": [
 147        "21661"
 148       ]
 149      },
 150      "execution_count": 82,
 151      "metadata": {},
 152      "output_type": "execute_result"
 153     }
 154    ],
 155    "source": [
 156     "word_sets = collections.defaultdict(set)\n",
 157     "for w in words:\n",
 158     "    letters = frozenset(w)\n",
 159     "    word_sets[letters].add(w)\n",
 160     "len(word_sets)"
 161    ]
 162   },
 163   {
 164    "cell_type": "code",
 165    "execution_count": 86,
 166    "id": "63121d2b",
 167    "metadata": {},
 168    "outputs": [
 169     {
 170      "data": {
 171       "text/plain": [
 172        "{'elephant', 'naphthalene', 'pentathlete'}"
 173       ]
 174      },
 175      "execution_count": 86,
 176      "metadata": {},
 177      "output_type": "execute_result"
 178     }
 179    ],
 180    "source": [
 181     "word_sets[frozenset('elephant')]"
 182    ]
 183   },
 184   {
 185    "cell_type": "code",
 186    "execution_count": 87,
 187    "id": "267130ba",
 188    "metadata": {},
 189    "outputs": [],
 190    "source": [
 191     "@dataclass(frozen=True)\n",
 192     "class Honeycomb():\n",
 193     "    mandatory: str\n",
 194     "    letters: frozenset\n",
 195     "      \n",
 196     "    def __repr__(self):\n",
 197     "        return f'{self.mandatory}|{\"\".join(sorted(self.letters - set(self.mandatory)))}'"
 198    ]
 199   },
 200   {
 201    "cell_type": "code",
 202    "execution_count": 88,
 203    "id": "0ca00165",
 204    "metadata": {},
 205    "outputs": [
 206     {
 207      "data": {
 208       "text/plain": [
 209        "g|aelmpx"
 210       ]
 211      },
 212      "execution_count": 88,
 213      "metadata": {},
 214      "output_type": "execute_result"
 215     }
 216    ],
 217    "source": [
 218     "honeycomb = Honeycomb(mandatory='g', letters=frozenset('apxmelg'))\n",
 219     "honeycomb"
 220    ]
 221   },
 222   {
 223    "cell_type": "code",
 224    "execution_count": 89,
 225    "id": "bb848e88",
 226    "metadata": {},
 227    "outputs": [],
 228    "source": [
 229     "def present(honeycomb, target):\n",
 230     "    return (honeycomb.mandatory in target) and target.issubset(honeycomb.letters)"
 231    ]
 232   },
 233   {
 234    "cell_type": "code",
 235    "execution_count": 90,
 236    "id": "add4f445",
 237    "metadata": {},
 238    "outputs": [
 239     {
 240      "data": {
 241       "text/plain": [
 242        "14"
 243       ]
 244      },
 245      "execution_count": 90,
 246      "metadata": {},
 247      "output_type": "execute_result"
 248     }
 249    ],
 250    "source": [
 251     "present_sets = [s for s in word_sets if present(honeycomb, s)]\n",
 252     "len(present_sets)"
 253    ]
 254   },
 255   {
 256    "cell_type": "code",
 257    "execution_count": 91,
 258    "id": "3354f6d7",
 259    "metadata": {},
 260    "outputs": [
 261     {
 262      "data": {
 263       "text/plain": [
 264        "[frozenset({'a', 'e', 'g', 'p'}),\n",
 265        " frozenset({'a', 'e', 'g', 'm'}),\n",
 266        " frozenset({'a', 'g', 'm'}),\n",
 267        " frozenset({'a', 'e', 'g', 'l', 'p'}),\n",
 268        " frozenset({'a', 'e', 'g', 'l'}),\n",
 269        " frozenset({'a', 'e', 'g'}),\n",
 270        " frozenset({'a', 'g', 'l'}),\n",
 271        " frozenset({'a', 'g', 'l', 'm'}),\n",
 272        " frozenset({'a', 'e', 'g', 'l', 'm'}),\n",
 273        " frozenset({'a', 'g'}),\n",
 274        " frozenset({'a', 'g', 'l', 'x'}),\n",
 275        " frozenset({'e', 'g', 'l'}),\n",
 276        " frozenset({'a', 'g', 'l', 'p'}),\n",
 277        " frozenset({'a', 'g', 'm', 'p'})]"
 278       ]
 279      },
 280      "execution_count": 91,
 281      "metadata": {},
 282      "output_type": "execute_result"
 283     }
 284    ],
 285    "source": [
 286     "present_sets"
 287    ]
 288   },
 289   {
 290    "cell_type": "code",
 291    "execution_count": 92,
 292    "id": "2e85ce06",
 293    "metadata": {},
 294    "outputs": [
 295     {
 296      "name": "stdout",
 297      "output_type": "stream",
 298      "text": [
 299       "{'peag', 'agapae', 'peage', 'gape', 'agape', 'page'}\n",
 300       "{'game', 'gemmae', 'mage', 'gemma'}\n",
 301       "{'magma', 'agma', 'agama', 'gamma', 'gama'}\n",
 302       "{'pelage', 'plage'}\n",
 303       "{'eagle', 'algae', 'galeae', 'aglee', 'allege', 'legal', 'galea', 'gale', 'gaggle', 'egal'}\n",
 304       "{'gage', 'agee'}\n",
 305       "{'gala', 'gall', 'alga', 'algal'}\n",
 306       "{'amalgam'}\n",
 307       "{'agleam', 'gleam'}\n",
 308       "{'gaga'}\n",
 309       "{'galax'}\n",
 310       "{'glee', 'gelee', 'gleg'}\n",
 311       "{'plagal'}\n",
 312       "{'gamp'}\n"
 313      ]
 314     }
 315    ],
 316    "source": [
 317     "for s in present_sets:\n",
 318     "    print(word_sets[s])"
 319    ]
 320   },
 321   {
 322    "cell_type": "code",
 323    "execution_count": 93,
 324    "id": "3c6f212e",
 325    "metadata": {},
 326    "outputs": [],
 327    "source": [
 328     "def score(present_set):\n",
 329     "    score = 0\n",
 330     "    for w in word_sets[present_set]:\n",
 331     "        if len(w) == 4:\n",
 332     "            score += 1\n",
 333     "        else:\n",
 334     "            score += len(w)\n",
 335     "    if len(present_set) == 7:\n",
 336     "        score += len(word_sets[present_set]) * 7\n",
 337     "    return score"
 338    ]
 339   },
 340   {
 341    "cell_type": "code",
 342    "execution_count": 94,
 343    "id": "01c3743c",
 344    "metadata": {},
 345    "outputs": [
 346     {
 347      "data": {
 348       "text/plain": [
 349        "153"
 350       ]
 351      },
 352      "execution_count": 94,
 353      "metadata": {},
 354      "output_type": "execute_result"
 355     }
 356    ],
 357    "source": [
 358     "sum(score(present_set) for present_set in present_sets)"
 359    ]
 360   },
 361   {
 362    "cell_type": "code",
 363    "execution_count": 95,
 364    "id": "1f45f6f5",
 365    "metadata": {},
 366    "outputs": [
 367     {
 368      "data": {
 369       "text/plain": [
 370        "False"
 371       ]
 372      },
 373      "execution_count": 95,
 374      "metadata": {},
 375      "output_type": "execute_result"
 376     }
 377    ],
 378    "source": [
 379     "set('megaplex') in words"
 380    ]
 381   },
 382   {
 383    "cell_type": "code",
 384    "execution_count": 96,
 385    "id": "979d9ed5",
 386    "metadata": {},
 387    "outputs": [],
 388    "source": [
 389     "scored_sets = {s: score(s) for s in word_sets}"
 390    ]
 391   },
 392   {
 393    "cell_type": "code",
 394    "execution_count": 97,
 395    "id": "790b7303",
 396    "metadata": {},
 397    "outputs": [
 398     {
 399      "name": "stdout",
 400      "output_type": "stream",
 401      "text": [
 402       "frozenset({'e', 'a', 'p', 'g'}) {'peag', 'agapae', 'peage', 'gape', 'agape', 'page'} 19 19\n",
 403       "frozenset({'m', 'a', 'e', 'g'}) {'game', 'gemmae', 'mage', 'gemma'} 13 13\n",
 404       "frozenset({'m', 'a', 'g'}) {'magma', 'agma', 'agama', 'gamma', 'gama'} 17 17\n",
 405       "frozenset({'p', 'l', 'a', 'g', 'e'}) {'pelage', 'plage'} 11 11\n",
 406       "frozenset({'a', 'l', 'e', 'g'}) {'eagle', 'algae', 'galeae', 'aglee', 'allege', 'legal', 'galea', 'gale', 'gaggle', 'egal'} 45 45\n",
 407       "frozenset({'a', 'e', 'g'}) {'gage', 'agee'} 2 2\n",
 408       "frozenset({'a', 'l', 'g'}) {'gala', 'gall', 'alga', 'algal'} 8 8\n",
 409       "frozenset({'m', 'a', 'l', 'g'}) {'amalgam'} 7 7\n",
 410       "frozenset({'m', 'a', 'l', 'g', 'e'}) {'agleam', 'gleam'} 11 11\n",
 411       "frozenset({'a', 'g'}) {'gaga'} 1 1\n",
 412       "frozenset({'a', 'l', 'x', 'g'}) {'galax'} 5 5\n",
 413       "frozenset({'l', 'e', 'g'}) {'glee', 'gelee', 'gleg'} 7 7\n",
 414       "frozenset({'l', 'a', 'p', 'g'}) {'plagal'} 6 6\n",
 415       "frozenset({'m', 'a', 'p', 'g'}) {'gamp'} 1 1\n"
 416      ]
 417     }
 418    ],
 419    "source": [
 420     "for s in present_sets:\n",
 421     "    print(s, word_sets[s], score(s), scored_sets[s])"
 422    ]
 423   },
 424   {
 425    "cell_type": "code",
 426    "execution_count": 98,
 427    "id": "78d423a5",
 428    "metadata": {},
 429    "outputs": [],
 430    "source": [
 431     "def score_honeycomb(honeycomb):\n",
 432     "    return sum(sc for letters, sc in scored_sets.items() \n",
 433     "               if honeycomb.mandatory in letters\n",
 434     "               if letters.issubset(honeycomb.letters)\n",
 435     "#                if present(honeycomb, letters)\n",
 436     "              )"
 437    ]
 438   },
 439   {
 440    "cell_type": "code",
 441    "execution_count": 99,
 442    "id": "3c7c7a83",
 443    "metadata": {},
 444    "outputs": [
 445     {
 446      "data": {
 447       "text/plain": [
 448        "153"
 449       ]
 450      },
 451      "execution_count": 99,
 452      "metadata": {},
 453      "output_type": "execute_result"
 454     }
 455    ],
 456    "source": [
 457     "score_honeycomb(honeycomb)"
 458    ]
 459   },
 460   {
 461    "cell_type": "code",
 462    "execution_count": 100,
 463    "id": "d53c4d64",
 464    "metadata": {},
 465    "outputs": [],
 466    "source": [
 467     "# hcs = []\n",
 468     "\n",
 469     "# for mand in 'abcde':\n",
 470     "#     remaining = set('abcde') - set(mand)\n",
 471     "#     for others in itertools.combinations(remaining, r=3):\n",
 472     "#         hcs.append(Honeycomb(mandatory=mand, letters=frozenset(others) | frozenset(mand)))\n",
 473     "\n",
 474     "# print(len(hcs))"
 475    ]
 476   },
 477   {
 478    "cell_type": "code",
 479    "execution_count": 101,
 480    "id": "d967a3df",
 481    "metadata": {},
 482    "outputs": [],
 483    "source": [
 484     "# hcs"
 485    ]
 486   },
 487   {
 488    "cell_type": "code",
 489    "execution_count": 102,
 490    "id": "4a07a6b7",
 491    "metadata": {},
 492    "outputs": [],
 493    "source": [
 494     "# honeycombs = []\n",
 495     "\n",
 496     "# for mand in string.ascii_lowercase:\n",
 497     "#     remaining = set(string.ascii_lowercase) - set(mand)\n",
 498     "#     for others in itertools.combinations(remaining, r=6):\n",
 499     "#         honeycombs.append(Honeycomb(mandatory=mand, letters=frozenset(others) | frozenset(mand)))\n",
 500     "\n",
 501     "# print(len(honeycombs))"
 502    ]
 503   },
 504   {
 505    "cell_type": "code",
 506    "execution_count": 103,
 507    "id": "14c38054",
 508    "metadata": {},
 509    "outputs": [],
 510    "source": [
 511     "# honeycombs = []\n",
 512     "\n",
 513     "# candidate_letters = set(string.ascii_lowercase)\n",
 514     "# candidate_letters.remove('s')\n",
 515     "# candidate_letters = frozenset(candidate_letters)\n",
 516     "\n",
 517     "# for mand in candidate_letters:\n",
 518     "#     remaining = candidate_letters - set(mand)\n",
 519     "#     for others in itertools.combinations(remaining, r=6):\n",
 520     "#         honeycombs.append(Honeycomb(mandatory=mand, letters=frozenset(others) | frozenset(mand)))\n",
 521     "\n",
 522     "# print(len(honeycombs))"
 523    ]
 524   },
 525   {
 526    "cell_type": "code",
 527    "execution_count": 104,
 528    "id": "f8ea5307",
 529    "metadata": {},
 530    "outputs": [],
 531    "source": [
 532     "# [(h, score_honeycomb(h)) for h in honeycombs[:5]]"
 533    ]
 534   },
 535   {
 536    "cell_type": "code",
 537    "execution_count": 105,
 538    "id": "4f2118dc",
 539    "metadata": {},
 540    "outputs": [],
 541    "source": [
 542     "# %%timeit\n",
 543     "# max(honeycombs, key=score_honeycomb)"
 544    ]
 545   },
 546   {
 547    "cell_type": "code",
 548    "execution_count": 106,
 549    "id": "febee1c1",
 550    "metadata": {},
 551    "outputs": [
 552     {
 553      "data": {
 554       "text/plain": [
 555        "7986"
 556       ]
 557      },
 558      "execution_count": 106,
 559      "metadata": {},
 560      "output_type": "execute_result"
 561     }
 562    ],
 563    "source": [
 564     "pangram_sets = [s for s in word_sets.keys() if len(s) == 7 if 's' not in s]\n",
 565     "len(pangram_sets)"
 566    ]
 567   },
 568   {
 569    "cell_type": "code",
 570    "execution_count": 107,
 571    "id": "54a06bdf",
 572    "metadata": {},
 573    "outputs": [
 574     {
 575      "name": "stdout",
 576      "output_type": "stream",
 577      "text": [
 578       "55902\n"
 579      ]
 580     }
 581    ],
 582    "source": [
 583     "ps_honeycombs = []\n",
 584     "\n",
 585     "for ps in pangram_sets:\n",
 586     "    for mand in ps:\n",
 587     "        ps_honeycombs.append(Honeycomb(mandatory=mand, letters=ps))\n",
 588     "\n",
 589     "print(len(ps_honeycombs))"
 590    ]
 591   },
 592   {
 593    "cell_type": "code",
 594    "execution_count": 108,
 595    "id": "301b3cd0",
 596    "metadata": {},
 597    "outputs": [],
 598    "source": [
 599     "# %%timeit\n",
 600     "# max(ps_honeycombs, key=score_honeycomb)"
 601    ]
 602   },
 603   {
 604    "cell_type": "code",
 605    "execution_count": 109,
 606    "id": "653613ac",
 607    "metadata": {},
 608    "outputs": [],
 609    "source": [
 610     "##  1 a,e,g,i,n,r,t r       3898\n",
 611     "##  2 a,e,g,i,n,r,t n       3782\n",
 612     "##  3 a,e,g,i,n,r,t e       3769"
 613    ]
 614   },
 615   {
 616    "cell_type": "code",
 617    "execution_count": 110,
 618    "id": "3cdbd956",
 619    "metadata": {},
 620    "outputs": [
 621     {
 622      "data": {
 623       "text/plain": [
 624        "3898"
 625       ]
 626      },
 627      "execution_count": 110,
 628      "metadata": {},
 629      "output_type": "execute_result"
 630     }
 631    ],
 632    "source": [
 633     "score_honeycomb(Honeycomb('r', frozenset('aeginrt')))"
 634    ]
 635   },
 636   {
 637    "cell_type": "code",
 638    "execution_count": 111,
 639    "id": "5f06f87b",
 640    "metadata": {},
 641    "outputs": [
 642     {
 643      "data": {
 644       "text/plain": [
 645        "3782"
 646       ]
 647      },
 648      "execution_count": 111,
 649      "metadata": {},
 650      "output_type": "execute_result"
 651     }
 652    ],
 653    "source": [
 654     "score_honeycomb(Honeycomb('n', frozenset('aeginrtn')))"
 655    ]
 656   },
 657   {
 658    "cell_type": "code",
 659    "execution_count": 112,
 660    "id": "ab6bc64e",
 661    "metadata": {},
 662    "outputs": [
 663     {
 664      "data": {
 665       "text/plain": [
 666        "3769"
 667       ]
 668      },
 669      "execution_count": 112,
 670      "metadata": {},
 671      "output_type": "execute_result"
 672     }
 673    ],
 674    "source": [
 675     "score_honeycomb(Honeycomb('e', frozenset('aeginrte')))"
 676    ]
 677   },
 678   {
 679    "cell_type": "code",
 680    "execution_count": 113,
 681    "id": "914fece8",
 682    "metadata": {},
 683    "outputs": [
 684     {
 685      "data": {
 686       "text/plain": [
 687        "26"
 688       ]
 689      },
 690      "execution_count": 113,
 691      "metadata": {},
 692      "output_type": "execute_result"
 693     }
 694    ],
 695    "source": [
 696     "partitioned_scored_sets = {l: {s: scored_sets[s] for s in scored_sets if l in s} \n",
 697     "                           for l in string.ascii_lowercase}\n",
 698     "len(partitioned_scored_sets)"
 699    ]
 700   },
 701   {
 702    "cell_type": "code",
 703    "execution_count": 114,
 704    "id": "f1454ccd",
 705    "metadata": {},
 706    "outputs": [],
 707    "source": [
 708     "def partitioned_score_honeycomb(honeycomb):\n",
 709     "    return sum(sc for letters, sc in partitioned_scored_sets[honeycomb.mandatory].items() \n",
 710     "               if letters.issubset(honeycomb.letters)\n",
 711     "              )"
 712    ]
 713   },
 714   {
 715    "cell_type": "code",
 716    "execution_count": 115,
 717    "id": "7380dbd6",
 718    "metadata": {},
 719    "outputs": [
 720     {
 721      "name": "stdout",
 722      "output_type": "stream",
 723      "text": [
 724       "r|aegint\n"
 725      ]
 726     }
 727    ],
 728    "source": [
 729     "# %%timeit\n",
 730     "print(max(ps_honeycombs, key=partitioned_score_honeycomb))"
 731    ]
 732   },
 733   {
 734    "cell_type": "code",
 735    "execution_count": 74,
 736    "id": "51d0317c",
 737    "metadata": {},
 738    "outputs": [
 739     {
 740      "data": {
 741       "text/plain": [
 742        "13"
 743       ]
 744      },
 745      "execution_count": 74,
 746      "metadata": {},
 747      "output_type": "execute_result"
 748     }
 749    ],
 750    "source": [
 751     "# partitioned_score_honeycomb(Honeycomb('a', 'abc'))"
 752    ]
 753   },
 754   {
 755    "cell_type": "code",
 756    "execution_count": 76,
 757    "id": "77d74a74-55e9-498b-abdf-b02c1f7f01a3",
 758    "metadata": {},
 759    "outputs": [
 760     {
 761      "data": {
 762       "text/plain": [
 763        "19941"
 764       ]
 765      },
 766      "execution_count": 76,
 767      "metadata": {},
 768      "output_type": "execute_result"
 769     }
 770    ],
 771    "source": [
 772     "# max(len(partitioned_scored_sets[k]) for k in partitioned_scored_sets)"
 773    ]
 774   },
 775   {
 776    "cell_type": "code",
 777    "execution_count": 77,
 778    "id": "35b58dec-7138-4fdb-86cc-80f3eb6a555a",
 779    "metadata": {},
 780    "outputs": [
 781     {
 782      "data": {
 783       "text/plain": [
 784        "37313"
 785       ]
 786      },
 787      "execution_count": 77,
 788      "metadata": {},
 789      "output_type": "execute_result"
 790     }
 791    ],
 792    "source": [
 793     "# len(scored_sets)"
 794    ]
 795   },
 796   {
 797    "cell_type": "code",
 798    "execution_count": null,
 799    "id": "7e4173b4-26a9-4198-b572-d57db321fe94",
 800    "metadata": {},
 801    "outputs": [],
 802    "source": []
 803   }
 804  ],
 805  "metadata": {
 806   "jupytext": {
 807    "formats": "ipynb,auto:light"
 808   },
 809   "kernelspec": {
 810    "display_name": "Python 3 (ipykernel)",
 811    "language": "python",
 812    "name": "python3"
 813   },
 814   "language_info": {
 815    "codemirror_mode": {
 816     "name": "ipython",
 817     "version": 3
 818    },
 819    "file_extension": ".py",
 820    "mimetype": "text/x-python",
 821    "name": "python",
 822    "nbconvert_exporter": "python",
 823    "pygments_lexer": "ipython3",
 824    "version": "3.8.8"
 825   }
 826  },
 827  "nbformat": 4,
 828  "nbformat_minor": 5
 829 }