Project Euler Problem 42 Solution


The nthn^{th} term of the sequence of triangle numbers is given by, tn=12n(n+1)t_n = \frac{1}{2}n(n+1); so the first ten triangle numbers are:

1,3,6,10,15,21,28,36,45,55,...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=t1019 + 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?