My entry into the pot works by starting with the smallest words and building to the largest, instead of the other way. On the word list from ITA, the answers are 16 letters long (Underestimations and indeterminations).

#!perl
use strict;
use Data::Dumper;
$|++;

my %WordTree = ();
my %WordLengths = ();
my $LongWordLength = 1;

open (DATA, "Word.txt");
while (<DATA>) {
    chomp;
    my $Word = $_;
    my $Length = length($_);
    next if $Length < 3;
    $LongWordLength = $Length if ($LongWordLength < $Length);
    push (@{$WordLengths{$Length}}, $Word);
}
print "Finished reading Data\n";
close (DATA);

for (my $CurrentLength = 3; $CurrentLength <= $LongWordLength; $Curren
+tLength++) {
    print "Working on words of length $CurrentLength\n";
    my ($Word) = "";
    foreach $Word (@{$WordLengths{$CurrentLength}}) {
        my (@SortedLetters) = sort split //, $Word;
        if ($CurrentLength > 3) {
            my $TempWord = "";
            my @SplicedLetters = "";
            my $MatchFlag = 0;
            for (my $Splice = 0; $Splice <= $#SortedLetters; $Splice++
+)  {
                @SplicedLetters = @SortedLetters;
                splice(@SplicedLetters, $Splice, 1);
                $TempWord = join '', @SplicedLetters;
                if (exists($WordTree{$#SortedLetters}->{$TempWord})) {
                    if (! exists($WordTree{$CurrentLength}->{join '', 
+@SortedLetters})) {
                        push (@{$WordTree{$CurrentLength}->{join '', @
+SortedLetters}}, $Word);
                        push (@{$WordTree{$CurrentLength}->{join '', @
+SortedLetters}},
                              @{$WordTree{$CurrentLength - 1}->{join '
+', @SplicedLetters}});
                    }
                    last;
                }                    
            }
        } else {
            if (! exists($WordTree{3}->{join '', @SortedLetters})) {
                push (@{$WordTree{3}->{join '', @SortedLetters}}, $Wor
+d);
            }
        }
    }
}

my (@LongestMatch) = sort {$a<=>$b} keys %WordTree;

my $NotFoundLongest = 1;
while ($NotFoundLongest && $#LongestMatch > 1) {
    if (keys %{$WordTree{$LongestMatch[$#LongestMatch]}} > 0) {
        print "The longest length is $LongestMatch[$#LongestMatch]\n";
        print Dumper $WordTree{pop @LongestMatch};
        $NotFoundLongest = 0;
    }
    pop @LongestMatch;
}
[download]