# Coded triangle numbers

Author: Shlomi Fish

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?

Source code: prob042-shlomif.p6

```use v6;

sub is_triangle(\$half)
{
my \$n = \$half +< 1;

my \$i = Int( sqrt(\$n) );

if \$i * \$i == \$n
{
return False;
}
return \$n == \$i * ( \$i + 1 );
}

sub MAIN(:\$verbose = False) {
my \$total_sum = 0;

my \$words-file = \$*SPEC.catdir(\$*PROGRAM-NAME.IO.dirname, 'words.txt');
my \$text = \$words-file.IO.slurp;
my @words = \$text ~~ m:global/<[A .. Z]>+/;
my \$RESULT = +(@words.grep(sub (\$_) { is_triangle( sum( map { \$_.ord - 'A'.ord + 1 },\$_.comb) ) }));
say \$RESULT;
}
```