It's always fun to watch a couple of big beasts snarling at each other and preparing to fight to the death. In the University Challenge corner, Jeremy Paxman, his eyebrow raised in horror as another batch of students fails to remember who was the only British Prime Minister to play first-class cricket (*see bottom for answer). And in the Mastermind corner, John Humphrys, just about managing to keep the pity out of his voice as he says the words every contestant dreads: "You passed on nine questions."

As you'd expect, Paxo started it. Speaking at the Cheltenham Literature Festival, where the public flocks to see famous people off the telly who might or might not have written any books, he denied suggestions that the questions on University Challenge were easier than they used to be. In fact, he said, they were much harder. Mastermind, on the other hand "has been getting a lot easier, as has been obvious."

Humphrys, who was also at Cheltenham, responded in kind. "Jeremy who?" he said, describing University Challenge as "fading" and making a passing reference to Paxman's underpants – literally, a blow below the belt. Anne Robinson, perhaps fortunately, wasn't available for comment.

But what is the truth of the matter? Are quiz shows dumbing down or clevering up? Wherever pub quizzers congregate – usually at a pub quiz, by odd coincidence – this debate seems to rage. One person will cite the fantastically lowbrow specialist subjects now selected on Mastermind – the life and works of Ozzy Osbourne, maybe, or the FA Cup Runs of Yeovil Town – while pointing out that no one knows any Greek or Latin any more.

Someone else will say, almost certainly truthfully, that the questions in the pub quiz they are attending are appreciably harder than they would have been 10 or 15 years ago. People know more, about a wider range of subjects, while knowing less about things we feel they should know about. And that's just a broad simplification of an argument that is impossible to resolve.

As it happens, I myself have been on University Challenge: four years ago, on the Private Eye team. With me were Ian Hislop, Francis Wheen and Christopher Booker, their three vast brains visibly bulging with knowledge. It was terrifying. The pressure was intense, the questions were infinitely harder than they are when you're watching it at home, and Paxman was relentless in his scorn when you got an easy one wrong. Which we all did, at least once.

A few years before, a contestant had said she needed to go to the loo halfway through recording, locked herself in and refused to come out. They had to complete the recording with an empty chair and superimpose her on afterwards.

The rather prosaic truth is that both programmes remain a fearsome challenge, as does The Weakest Link, for slightly different, Botox-related reasons. All three keep the Eye's "Dumb Britain" column well supplied with examples of people making complete fools of themselves on quiz shows. Much as Paxo and Humphrys did over the weekend, now I think about it.

* Sir Alec Douglas-Home

Marcus Berkmann's books include The Prince of Wales (Highgate) Pub Quiz Book, published by Hodder and Stoughton