alice-bob.ipynb

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   "source": [
    "from collections import defaultdict\n",
    "s = defaultdict(list) # sums\n",
    "p = defaultdict(list) # products"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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     "data": {
      "text/plain": [
       "(96, 1179)"
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     "execution_count": 2,
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   "source": [
    "# Indexing pairs by their sums and products\n",
    "for x in range(2, 100):\n",
    "    for y in range(x + 1, 100 - x + 1):\n",
    "        s[x + y].append((x, y))\n",
    "        p[x * y].append((x, y))\n",
    "len(s), len(p)"
   ]
  },
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   "cell_type": "code",
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   "source": [
    "# Keeping only the sums and products that have several pairs that could have generated them\n",
    "# Alice says she doesn't know (and Bob doesn't know yet)\n",
    "p2 = {k: v for k, v in p.items() if len(v) > 1}\n",
    "len(p2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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     "execution_count": 4,
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   ],
   "source": [
    "# Bob says he knew alice didn't know, so it means all the pairs he has have products\n",
    "# that could be generated by other pairs\n",
    "s2 = {k: v for k, v in s.items() if all(len(p.get(a*b, []))>1 for a, b in v)}\n",
    "len(s2)"
   ]
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       "86"
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     "execution_count": 5,
     "metadata": {},
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   ],
   "source": [
    "# Alice says she now knows, which means she has a product that only has one value from s2\n",
    "s2set = set(a for b in s2.values() for a in b)\n",
    "p3set = {e.pop() for e in (set(v) & s2set for v in p2.values()) if len(e) == 1}\n",
    "len(p3set)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Bob says he knows too, which means he has a sum that only has one value from p3\n",
    "s3set = {e.pop() for e in (set(v) & p3set for v in s2.values()) if len(e) == 1}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(4, 13)}"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "s3set"
   ]
  }
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