"What word in the English language has 15 letters, none of which is repeated?"

This was the question on the blackboard in a local branch of a well-known purveyor of over-priced, burnt coffee, and if you knew the answer you could get a free latte. I though to myself "Perl could help find the answer to that", and I set about writing the following code:
#!/usr/bin/perl -w

use strict;
use diagnostics;

# open DICT, "/usr/dict/words";
open DICT, "/tmp/web2.txt";
my @words_of_15_letters;

while (<DICT>) {
  push @words_of_15_letters, $_ if /^.{15}$/;
}

print "Number of words found ", scalar @words_of_15_letters, "\n";

foreach my $word (@words_of_15_letters) {

  my %letter_count;
  my $repeat_found;

  foreach my $letter (split //, $word) {
    $letter_count{$letter}++;
  }

  foreach (keys %letter_count) {
    $repeat_found = 1 if $letter_count{$_} > 1;
  }

  print $word unless $repeat_found;
}

[download]

The first thing I found was that /usr/dict/words doesn't have the answer. It has too few words in it. I downloaded a dictionary file from puzzlers.org that had about 5 times more words in it.

This code finds the right answer, but I would like to know if anyone can improve it. It seems much more long-winded than it needs to be. Is there any way of making it more succinct? In particular, is there a way to check for repeated letters in the pattern match?

In reply to Coffee time quiz by perlmoth

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