# Coded triangle numbers (Euler Problem 42)¶

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The nth term of the sequence of triangle numbers is given by, $t_n = \frac{1}{2}n(n+1)$; so the first ten triangle numbers are:

    1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

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.

Using 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? (The file is saved in the same directory as this notebook file as EulerProblem042.txt)

In [1]:

    def get_words():
        with open("EulerProblem042.txt", "r") as f:
            s = f.read()
        words = [w.strip('"') for w in s.split(",")]
        return words

    def calculate_word_value(word):
        word = word.upper()
        return sum([ord(letter) - 64 for letter in word])

    assert(calculate_word_value("sky") == 55)

    def get_triangle_numbers(n):
        return {n * (n + 1) // 2 for n in range(1, 101)}

In [2]:

    triangle_numbers = get_triangle_numbers(100)

    s = len([word for word in get_words() if calculate_word_value(word) in triangle_numbers])
    assert(s == 162)
    print(s)

    162

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