The nth term of the sequence of triangle numbers is given by, tn = 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 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 Data.Char triangle =[n*(n+1)`div`2|n<-[1..]] isIn (x:xs) y | x == y = True | x < y =isIn xs y | x > y = False value =sum.map (v.toUpper) where v = flip (-) (ord 'A' - 1).ord isTriangle = isIn triangle . value main =getContents>>=print.length.filter isTriangle.(read::String->[String])