Not the first time this has happened.
I've seen quite a few episodes in the past where the answer evaded Rachel and even Ms Vorderman!
I remember once, when Carol said that she couldn't find an answer and Richard Whiteley had done it...he was able to sit there and dictate how to reach the answer and of course, he got an enormous round of applause!
CECIL generates a random number. It's not always possible to reach the target but I'm not sure how they would know so quickly that it's impossible (unless it's obvious).
No, it's random. When I first saw it I thought the cards had something embedded in it so the computer knew what to use in it's algorithm, but apparently it's simpler than that.
Captain - what swish technology do you mean? All you need is someone typing the numbers into a computer as the cards are turned up and it's job done. Computers in 1982 were easily capable of doing the necessary sums.