## Coded triangle numbers

### Problem 42

Published on Friday, 25th April 2003, 06:00 pm; Solved by 46144; Difficulty rating: 5%The *n*^{th} term of the sequence of triangle numbers is given by, *t _{n}* = ½

*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?