# Project Euler Problem 42: Coded Triangle Numbers¶

The source code for this problem can be found here.

## Problem Statement¶

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

$1, 3, 6, 10, 15, 21, 28, 36, 45, 55, \dots$

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?

## Solution Discussion¶

Nothing sophisticated here, just map each word to the corresponding number and test whether it is a triangular number and then count them.

## Solution Implementation¶

from lib.sequence import Triangulars

def is_triangle_word(word: str) -> bool:
""" Check whether word is a triangle word

:param word: the word to test
:return: whether word is a triangle word or not
"""

mapping = {chr(i): i - ord('A') + 1 for i in range(ord('A'), ord('Z') + 1)}
word_value = sum([mapping[letter] for letter in word])
return word_value in Triangulars()

def solve():
""" Compute the answer to Project Euler's problem #42 """
words = [word.strip("\"") for word in words]  # strip quotes off each word
triangle_words = filter(is_triangle_word, words)
answer = len(list(triangle_words))  # number of triangle words

solutions.problem42.is_triangle_word(word)
Parameters: word (str) – the word to test bool whether word is a triangle word or not
solutions.problem42.solve()