Nerf Puzzle.ipynb

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    "from math import prod\n",
    "from random import choice, choices, shuffle\n",
    "\n",
    "primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199]    \n",
    "# A function to print all prime factors of  \n",
    "# a given number n \n",
    "def prime_factors(n):\n",
    "    \"\"\"returns a list of prime factors of n\"\"\"\n",
    "    p = 0 # in case primes seq empty\n",
    "    factors = []\n",
    "    for p in primes: \n",
    "        while n % p == 0:\n",
    "            n /= p\n",
    "            factors.append(int(p))\n",
    "        if n < p*p:\n",
    "            if n > 1:\n",
    "                factors.append(int(n))\n",
    "            return factors\n",
    "    return factors"
   ]
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   "metadata": {},
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   "source": [
    "def nerf(a, b):\n",
    "    afs = prime_factors(a)\n",
    "    afs = (n for n in afs)\n",
    "    bfs = prime_factors(b)\n",
    "    bfs = (n for n in bfs)\n",
    "\n",
    "    shared = []\n",
    "    not_shared = []\n",
    "    af = next(afs)\n",
    "    bf = next(bfs)\n",
    "    try:\n",
    "        while True:\n",
    "            if af<bf:\n",
    "                not_shared.append(af)\n",
    "                af = None\n",
    "                af = next(afs)\n",
    "            if af==bf:\n",
    "                shared.append(af)\n",
    "                shared.append(bf)\n",
    "                af = None\n",
    "                bf = None\n",
    "                af = next(afs)\n",
    "                bf = next(bfs)\n",
    "            if af>bf:\n",
    "                not_shared.append(bf)\n",
    "                bf = None\n",
    "                bf = next(bfs)\n",
    "    except StopIteration:\n",
    "        pass\n",
    "    \n",
    "    if af:\n",
    "        not_shared.append(af)\n",
    "        \n",
    "    if bf:\n",
    "        not_shared.append(bf)\n",
    "\n",
    "    for af in afs:\n",
    "        not_shared.append(af)\n",
    "\n",
    "    for bf in bfs:\n",
    "        not_shared.append(bf)  \n",
    "        \n",
    "    return prod(not_shared), prod(shared)"
   ]
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   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def start_game(nth_prime):\n",
    "\n",
    "    some_primes = primes[:nth_prime]\n",
    "    number = choice(some_primes)\n",
    "\n",
    "    print(f'starting game')\n",
    "    print(f'goal: nerf your number with one of the choices to try and build a number whos factors are {some_primes}\\n')\n",
    "\n",
    "    while True:\n",
    "        factors = prime_factors(number)\n",
    "        non_factors = list(set(some_primes).difference(factors))\n",
    "        if not(non_factors):\n",
    "            print(f'you win\\nfinal number = {number}')\n",
    "            break\n",
    "\n",
    "        num_factors = min(len(factors),3)\n",
    "\n",
    "        pickfrom = [\n",
    "            prod(choices(non_factors, k=num_factors)), \n",
    "            prod(choices(factors, k=num_factors-1) + choices(non_factors, k=1)),\n",
    "        ]\n",
    "        shuffle(pickfrom)\n",
    "        print(f'your number: {number}\\n\\ta: nerf with {pickfrom[0]}\\n\\tb: nerf with {pickfrom[1]}\\n\\tx: give up')\n",
    "        resp = input()\n",
    "        if resp == 'x':\n",
    "            print('give up')\n",
    "            break\n",
    "        if resp == 'a':\n",
    "            number = nerf(number, pickfrom[0])[0]\n",
    "        if resp == 'b':\n",
    "            number = nerf(number, pickfrom[1])[0]"
   ]
  },
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   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "starting game\n",
      "goal: nerf your number with one of the choices to try and build a number whos factors are [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]\n",
      "\n",
      "your number: 19\n",
      "\ta: nerf with 11\n",
      "\tb: nerf with 13\n",
      "\tx: give up\n",
      "a\n",
      "your number: 209\n",
      "\ta: nerf with 247\n",
      "\tb: nerf with 35\n",
      "\tx: give up\n",
      "b\n",
      "your number: 7315\n",
      "\ta: nerf with 75\n",
      "\tb: nerf with 6409\n",
      "\tx: give up\n",
      "b\n",
      "your number: 46881835\n",
      "\ta: nerf with 138\n",
      "\tb: nerf with 3289\n",
      "\tx: give up\n",
      "b\n",
      "your number: 7540435\n",
      "\ta: nerf with 70\n",
      "\tb: nerf with 286\n",
      "\tx: give up\n",
      "b\n",
      "your number: 2156564410\n",
      "\ta: nerf with 27\n",
      "\tb: nerf with 78\n",
      "\tx: give up\n",
      "b\n",
      "your number: 248834355\n",
      "\ta: nerf with 578\n",
      "\tb: nerf with 338\n",
      "\tx: give up\n",
      "b\n",
      "you win\n",
      "final number = 84106011990\n"
     ]
    }
   ],
   "source": [
    "start_game(10)"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
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   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
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   "source": []
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