Euler 042 - Coded triangle numbers.ipynb

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    "Euler Problem 42\n",
    "================\n",
    "\n",
    "The nth term of the sequence of triangle numbers is given by, $t_n = \\frac12 n(n+1)$; so the first ten triangle numbers are:\n",
    "\n",
    "    1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...\n",
    "\n",
    "By converting each letter in a word to a number corresponding to its alphabetical position and adding these values we form a word value. For example, the word value for `SKY` is $19 + 11 + 25 = 55 = t_{10}$. If the word value is a triangle number then we shall call the word a triangle word.\n",
    "\n",
    "Using [words.txt](files/p042_words.txt) (right click and 'Save Link/Target As...'), a 16K text file containing nearly two-thousand common English words, how many are triangle words?"
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      "162\n"
     ]
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   "source": [
    "def wordsum(word):\n",
    "    return sum(ord(w) for w in word) - 64*len(word)\n",
    "\n",
    "triangle_numbers = set(n*(n+1)/2 for n in range(1, 50))\n",
    "with open(\"data/p042_words.txt\", \"r\") as f:\n",
    "    words = f.readline().replace('\"','').split(',')\n",
    "    print(sum(wordsum(word) in triangle_numbers for word in words))"
   ]
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