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:
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?
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def wordsum(word):
return sum(ord(w) for w in word) - 64*len(word)
triangle_numbers = set(n*(n+1)/2 for n in range(1, 50))
with open("data/p042_words.txt", "r") as f:
words = f.readline().replace('"','').split(',')
print(sum(wordsum(word) in triangle_numbers for word in words))
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