## Problem:

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?

162

## Code:The solution may include methods that will be found here: Library.java .

public interface EulerSolution{

public String run();

}
/*
* Solution to Project Euler problem 42
* By Nayuki Minase
*
* http://nayuki.eigenstate.org/page/project-euler-solutions
* https://github.com/nayuki/Project-Euler-solutions
*/

public final class p042 implements EulerSolution {

public static void main(String[] args) {
System.out.println(new p042().run());
}

public String run() {
int count = 0;
for (String word : WORDS) {
if (isTriangularNumber(wordValue(word)))
count++;
}
return Integer.toString(count);
}

private static boolean isTriangularNumber(int x) {
for (int i = 1; ; i++) {
int t = i * (i + 1) / 2;
if (t == x)
return true;
if (t > x)
return false;
}
}

private static int wordValue(String s) {
int sum = 0;
for (int i = 0; i < s.length(); i++) {
char c = s.charAt(i);
if (c < 'A' || c > 'Z')
throw new IllegalArgumentException();
sum += c - 'A' + 1;
}
return sum;
}

}