eulerbooks/notebooks/problem0042.ipynb

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   "metadata": {},
   "source": [
    "# [Coded Triangle Numbers](https://projecteuler.net/problem=42)"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "First we read in the words:"
   ]
  },
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   "outputs": [],
   "source": [
    "with open(\"txt/0042_words.txt\") as f:\n",
    "    words = {w.strip('\"') for w in f.read().split(\",\")}"
   ]
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   "cell_type": "markdown",
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   "source": [
    "We'll also write a simple function for testing if a word is a \"triangle word\". We'll make use of SageMath's built-in function for testing if a number is triangular."
   ]
  },
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   "cell_type": "code",
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   "id": "313a760f",
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   "outputs": [],
   "source": [
    "def is_triangle_word(word):\n",
    "    value = sum(ord(c) - ord('A') + 1 for c in word)\n",
    "    return is_triangular_number(value)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba53d2b1",
   "metadata": {},
   "source": [
    "(It's not difficult to apply the quadratic formula to write our own test for [triangular numbers](https://en.wikipedia.org/wiki/Triangular_number).)\n",
    "\n",
    "Now we just test each word."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "14a9ea9a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "162"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "triangle_words = {w for w in words if is_triangle_word(w)}\n",
    "len(triangle_words)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02bf08bf",
   "metadata": {},
   "source": [
    "#### Copyright (C) 2025 filifa\n",
    "\n",
    "This work is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International license](https://creativecommons.org/licenses/by-sa/4.0/) and the [BSD Zero Clause license](https://spdx.org/licenses/0BSD.html)."
   ]
  }
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