Well, here's my solution:

use strict;
use warnings;
use 5.010;

open my $dfd, '<', '/usr/share/dict/british-english' or die $!;
my %dict;
while (<$dfd>) {
    next unless /^[a-z]+$/;
    push @{$dict{hash($_)}}, $_;
}
close $dfd;

while (<>) {
    exit if /^$/;
    say join '', @{$dict{hash($_)}} if $dict{hash($_)};
}

sub hash {
    join '', sort split //, shift;
}
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Wow, well thanks a lot, your solution is a lot more eloquent than mine would have been. Surprisingly fast to. I follow it for the most part but I get tripped up in a couple of places. If I am not mistaken you are opening the dictionary as output, loads all the words into a hash. Then gets input...but what exactly are you doing here?  say join '', @($dict{hash($_)}} if $dict{hash($_)}; Thanks for the help.

If you don't understand a data structure, you should use Data::Dumper.

If the dictionary contained

act
cat
dog
god
zebra
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It builds the following hash

%dict = (
    act   => [ 'act', 'cat' ],
    dgo   => [ 'dog', 'god' ],
    aberz => [ 'zebra'      ],
);
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If the user enters dog, it searches for dgo (hash("dog")) and lists what it finds (dog and god).

?node_id=3989;HIT=anagram;xs=1;re=N;U

Try Bugs Gore He It leaves it to the human to permute the words.

Some very interesting combinations in Anagram Hall of Fame and often very apt or comical. The Morse Code = Here Come Dots

I don't see a computer algorithm

It doesn't mean it doesn't exist

(Oops, redundant post)