I think it is one of those things where your brain gets trained and accustomed to seeing patterns as you do more and more.
Many years ago when I first met my wife-to-be, she would often do the Times Crossword (the cryptic one) and I tried to help.
Initially I couldn't make much sense of it. She would come up with answers and have to explain how she came up with them. After some time I cam accustomed to the language used and could do it on my own.
I think the same is true of Countdown. Play Scrabble and you will probably be rubbish. But play it everyday and you will begin to see patterns of letters that form reusable syllables which you can join together to make words.
Not sure if he is still on, but last week there was a 15 or 16 year old boy who could solve the conumdrums before the countdown clock had barely moved. I can't beleive he had time to work those out - more likely that he has done so many of them - perhaps he has countdown quiz books that the patterns just stick in his head and are instantly recognisable.
I often wonder whether being 'random' the numbers round ever comes out with combinations that are totally obvious such as
Target = 400
Numbers = 100, 50, 9, 7, 4, 1
Or whether the target number isn't random at all.
Or whether, being recorded they stop the show and re-run the target number generator.
Cheers,
Nigel