use strict;
use Algorithm::Loops qw( NextPermute );

$|= 1;
my %map;
@map{1..9,'a'..'f'}= reverse 1..9,'a'..'f';
my @digs= reverse 1..9,'a'..'f';

sub Biggest {
    my( $len, @toks )= @_;
    do {
        my $hex= join '', @map{ @toks[0..$len-1] };
        my $num;
        if( $len <= 8 ) {
            $num= hex $hex;
        } else {
            $num= hex substr( $hex, 0, 7 );
            $num *= 16   for  9..$len;
            $num += hex substr( $hex, 8, -1 );
        }
        for( $hex =~ /./g, 0 ) {
            if(  ! $_  ) {
                print "$hex\n";
                return;
            }
            last   if  0 != $num % hex($_);
        }
        @toks[ $len .. $#toks ]= reverse @toks[ $len .. $#toks ]
            if  $len < $#toks;
    } while( NextPermute(@toks) );
    @toks= @map{ @toks };
    print "No solution for $len of hexits: @toks\n";
}

for my $len ( 1..@digs ) {
    Biggest( $len, @map{ @digs } );
}
[download]