Problem 42

Problem 42

25 April 2003

The n^th term of the sequence of triangle numbers is given by, t_n = ½n(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 = t₁₀. If the word value is a triangle number then we shall call the word a triangle word.

Using (right click and 'Save Link/Target As...'), a 16K text file containing nearly two-thousand common English words, how many are triangle words?

def fun42():
    fp     = open("42.txt")
    words  = fp.readline().split(",")
    words  = [i[1:-1].upper() for i in words]
    result = 0
    for word in words:
        value = 0
        for i in word:
            value += (ord(i) - 64)
        value *= 2
        t      = int(math.sqrt(value))
        if t*(t+1) == value:
           result += 1
    fp.close()
    return result

answer is 162
time:0.0159997940063