Problem 42

Solution to Problem 42. Written in Python.

Problem: The n^th term of the sequence of triangle numbers is given by, tn = 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 = t₁₀. 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?

import csv
import os

file_path = os.path.join(os.path.dirname(__file__), '..', 'euler_lib/p042_words.txt')

get_num = lambda word: sum(["-ABCDEFGHIJKLMNOPQRSTUVWXYZ".index(char) for char in word])
tri = lambda n: n * (n + 1) / 2

tri_list = [tri(n) for n in range(1, 100)]

with open(file_path, 'r') as text_file:
    rows = csv.reader(text_file, delimiter=',', quotechar='"')
    words = [word for row in rows for word in row]

print len([word for word in words if get_num(word) in tri_list])