Project Euler Problem 042


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


Straight-forward solution:

alphabetical_value = lambda name: sum(ord(c) - 64 for c in name)
if __name__ == '__main__':    
    f = open('words.txt', 'r')
    s = f.readline()
    lst = s.replace("\"", "").split(",")
    triangles = set(n * (n + 1) // 2 for n in range(1,1000))
    result = sum(1 for name in lst if alphabetical_value(name) in triangles)
    print("The result is:", result)

The Python file is available for download here.

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