Radio Codes: Like Puzzles?

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. :D 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.

there's a good probability that, either on a tag or written in permanent marker on the inside of your tool kit, the radio code for the original car's radio is present. check there for a 5 digit code for $hits and giggles first. i didn't think it was the case with my car until one day, when putting an item back into the kit, i saw something in marker written in the case and said to myself : how neat! this 5 digit number must have some significance for it to be both the radio code and written in the tool box for some reason :D

good at the lottery? Looks like 1 of 500,000 posibilities to me...lol;)

Even if you have no idea what the code might be, that still only leaves a 5 digit number in which all of the numbers have to be 1-6. That gives us;

6*6*6*6*6=7776 possibilities

Now assuming that those numbers I found are the five numbers in the code, that narrows it down, since you only use each number once;

5*4*3*2*1=120 possibilities

And since '1' is used twice, I guess that number can be cut in half to 60? I'm not sure how that works. (edit: 5!/2!=60 possibilities :) )

Now also assuming the numbers were arranged in some way that the code could be figured out from them, that would hypothetically limit the possibilities to 15 or so. I've tried the first two with no luck, I guess while I'm waiting for the next hour to pass I can search around in the trunk. :D