I believe it was ”pick a number, any number” which was disclosed by Marvin quite early on, apparently as an easter egg. I read something explaining this somewhere ... don’t have the link to hand ...

Yes it is; in base 13. :-) [1]

[1] http://www.6times9.com/

The miniseries ends with that reveal, and Arthur quips “I always knew there was something fundamentally wrong with the universe.”

The programming joke goes something like this:

  #define SIX 1+5
  #define NINE 8+1
  return SIX*NINE;

Well, on yet another level, isn't the universe - at least, as far as it's limited to our own human condition - all about wrong answers?

In the TV show, near the end you can just about hear the strains of Bob Dylan singing "How many roads must a man walk down....".

That's on IIRC the Earth 2 in its very early existence and Arthur and Ford start pulling scrabble letters from the bag...

I guess it has a few million years to run to resolve to the correct question. :)

Presumably the mice would then require a third supercomputer to tell them why this is the most important question of life, the universe, and - you know - everything.