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ZFR: Pinging you, since you expressed interest.
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babark: Seems like an interesting intellectual exercise, and I might attempt it later anyway, but my laptop is away on R&R till Thursday, and I'm not sure I'm hard-core enough to attempt it on pen and paper.
Bump. How is it going?

Waiting on anyone else?
babark told me he might need some time to get a working solution and that I shouldn't wait for him.

However, pastebin has a limit on number of pastes per day, and I want to put all solutions and their results up in nice formatted code. So, please wait. I'll post all solutions today evening.
So. Here are the solutions I received. I grouped them by language so it's easier to compare.
Note that pastebin removes a newlines at the end. You may assume there is one unless otherwise specified. Some solutions depend on there not being one, while others depend on there being one, and for others still it doesn't matter. If B has to end with a newline it has to be produced in code A, or, if the language allows it, you can add a newline at the beginning of A.

C++ by Lillesort
Output
Final concatenation (BAB)

F# by Lillesort
Output
Final concatenation (BAB)
Note: Neither A nor B end in a newline.
ZFR says: My favourite solution. But it could be because I'm partial to the language. I love the way + was changed and how the comments were inserted in the final concatenation.

Python 3 by Lillesort
Output
Final concatenation (BAB)

TeX by Lillesort
Output
Final concatenation (BAB)
Note: Works with TeX only, not LaTeX. Page number is not considered as part of the output.
ZFR says: I have a feeling this is a very clever solution, but I'm not familiar with the language to give it its proper appreciation.

JavaScript by Lillesort
Output
Final concatenation (BAB)

JavaScript by adaliabooks
Output
Final concatenation (BAB)
Note: Depends on the text not being present in the console window earlier. Will not produce correct results if run twice in same console.

Bash by Lillesort
Output
Final concatenation (BAB)

C by Lillesort
Output
Final concatenation (BAB)
ZFR says: Wow. Just wow. Brilliant in its simplicity. The only non-esoteric solution not to rely on an if statement and the non-esoteric solution with the shortest B (3 characters). I love it.

Befunge by ZFR
Output
Final concatenation (BAB)
ZFR says: The output is just a single letter 'v'. The first one is needed to change paths and the one at the end needed to terminate, otherwise it enters an endless loop and keeps printing the code.

Another Befunge by ZFR
Output
Final concatenation (BAB)
ZFR says: Just a tiny variation on the above. BA still enters an endless loop, but doesn't print anything in it.

Befunge by Lillesort
Output
Final concatenation (BAB)
ZFR says: Lillesort learnt Befunge for this challenge. Nice. No endless loops here.

Another Befunge by Lillesort
Output
Final concatenation (BAB)
ZFR says: Uses self-modifying code. Very nice!

AsciiDots by adaliabooks
Output
Final concatenation (BAB)
ZFR says: adaliabooks learnt AsciiDots for this challenge. It's an interesting esoteric language. Note that there is a newline at the beginning (and end of) A, since B doesn't have one. More info on the language here:
http://ajanse.me/asciidots/language.html
Online interpreters:
http://ajanse.me/asciidots/demo/
https://tio.run/#asciidots

Another AsciiDots by adaliabooks
Output
Final concatenation (BAB)
ZFR says: Love the GOG logo in ASCII art. BAB produces a different code (8F489-2N4NW-74G56-71G17), but it's possible to change it by changing the warp letters. Some online interpreters have problem outputting all characters. The one at tio.run outputs A properly, while the one at ajanse.me outputs BAB properly.

Scilab by foxgog
Output
Final concatenation (BAB)

Windows batch by truhlik
Output
Final concatenation (BAB)
ZFR says: Nice obfuscation. The only non-esoteric language where you can't get the solution code by quickly looking at the source. BAB produces "GoG code is:=937D6-DBA97-CE394-F2F16 :)"
Post edited November 07, 2018 by ZFR
random.org selected adaliabooks as the winner of the GA. 8$ GOG games.

Submission(s) Most Liked By Judge(s) award goes to Lillesort. 3$ GOG games.

I've contacted you by PM for your prizes.

Thanks all for participating. I enjoyed going through your solutions. Some relly ingenious code there.
Post edited November 05, 2018 by ZFR
Congratulations to adaliabooks!

Also, thanks to ZFR for making this challenge; it was very fun to solve.
Thanks ZFR for hosting this challenge, I really enjoyed it.

I feel a little like I've robbed Lillesort131 though, I was sure they would win even just by pure numbers (even more so now that I've seen their solutions, I don't even understand half of them).

Like ZFR I really like the C solution, I'd toyed with the idea of something that commented out the middle section to work, but that is beautiful and brilliant.

I also like truhlik's batch solution... I have no idea what it does but it's impressive.
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Lillesort131: Congratulations to adaliabooks!

Also, thanks to ZFR for making this challenge; it was very fun to solve.
Hey, sorry to nudge you this way, but not sure if you're receiving my PMs.

Your prize is still not claimed. Anything from the Christmas sale?
Post edited December 21, 2018 by ZFR
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Lillesort131: Congratulations to adaliabooks!

Also, thanks to ZFR for making this challenge; it was very fun to solve.
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ZFR: Hey, sorry to nudge you this way, but not sure if you're receiving my PMs.

Your prize is still not claimed. Anything from the Christmas sale?
Sorry, haven't had time to respond until now, but I did indeed receive your PM. Anyway, I have sent you a response now, thank you again. ☺