Radio Codes: Like Puzzles?

[AWDSM]

I've only had this car for a month, and I reset the radio trying to get it to control the CD changer in the trunk. Now its asking for the security code. The radio is the KE83zbm cassette player but the sticker with the serial number is gone. I called BMW and they were able retrieve the code from the VIN number, but I don't think this is the factory radio (the harness is pretty hacked up) and the code hasn't worked. I pulled the cover off to see if the serial number might be inside somewhere, and found these numbers.

3A1653
JGZ

I'm assuming that is the model number. There were, however, five other numbers (all lower than 6) handwritten in red and blue ink. Coincidence? Here are the numbers in their original color and configuration.

. 1
1
. 3
2
. 6

So here is a list of possible answers I have started:

12136
12631
21136
21631
13612
13621
63112
63121

11326
62311

Now the last two are probably too simple, unless the colors are there simply to throw us off, but that may be over-thinking things a bit. The trick would have to be easy enough to remember after years of not thinking about it, so its probably not anything too complicated. I can only try three at a time, then have to wait an hour, but at least this narrows it down from 7776 possibilities to 120, and the arrangement above should bring that down to less than 20. Anyone have any insights? Or maybe some other way to retrieve the serial number? Thanks.