I don't really understand why a number would be "unknown", and consequently can't address where to place "?" characters. But that aside, this looks to me like a problem of enumerating all possible bit patterns for a ten-bit register. And since ten bits is within the realm of simple Perl integers, you can just iterate over every value from 0 through 2**11-1 and inflate its bit pattern into your original ATATGCGCAT string. This will assure that all possible combinations are enumerated. Here's one way to do that:

use strict;
use warnings;

my $string = 'ATATGCGCAT';

for my $num (0 .. 2**11 - 1) {
  print "$num: ",
    join('',
      map { substr($string, $_, 1) . ($num & (2**(9 - $_)) ? '2' : '1'
+); }
      0 .. 9
    ), "\n";
}
[download]

Here we're running through two loops. The outer loop simply iterates over every integer from 0 through 2 ** 11 - 1. That's how we generate our bit patterns. Then another loop maps the bit values into the original string. Finally, each pattern is printed.

The output will look like this:

2039: A2T2A2T2G2C2G1C2A2T2
2040: A2T2A2T2G2C2G2C1A1T1
2041: A2T2A2T2G2C2G2C1A1T2
2042: A2T2A2T2G2C2G2C1A2T1
2043: A2T2A2T2G2C2G2C1A2T2
2044: A2T2A2T2G2C2G2C2A1T1
2045: A2T2A2T2G2C2G2C2A1T2
2046: A2T2A2T2G2C2G2C2A2T1
2047: A2T2A2T2G2C2G2C2A2T2
[download]

I hope I understood the problem. ;)