Must you use a regular expression? If not, this works: 
#!/usr/bin/perl
use warnings;
use strict;

my @teststrings = qw(ABCXXXXXX AXCXXXXXX AXXDXFXXX AXXXXXXHI XXXXXXGHI
+ XXXXXXXXX AXXXXXXXI);

my $pattern = "ABCDEFGHI";
my $desired_matches = 3;

for (@teststrings) {
   my $result = $pattern ^ $_;
   my $matches = $result =~ tr/\0/ /;
   print "$_\n" if $matches == $desired_matches;
}

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In reply to Re: How to use regular expression for this? by AReed
in thread How to use regular expression for this? by davidz2f

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