John Humphrys has challenged Jeremy Paxman to a televised “general knowledge shoot-out” after the host of University Challenge accused his show, Mastermind, of dumbing down.

The dispute between the BBC presenters began at The Times Cheltenham Festival of Literature on Saturday, when a member of the public asked Paxman whether he believed that questions on University Challenge, which he has hosted since 1994, had become easier.

He said that questions had been “dumbed up”. Producers had compared the current crop of questions with those from the 1960s, when it was hosted by Bamber Gascoigne.

“I can show you questions from the early years of University Challenge and ones now and you can see for yourself,” he said.

“On the whole, questions are more difficult now than they used to be, much more difficult. This is a disgraceful canard put about by some old codgers. It is, however, true that they’ve got a lot easier on Mastermind.”

A question from University Challenge this year was: A baker makes between 30 and 50 scones. If he packs them in fives, he has one left over. If he packs them in threes, he has two left over. How many scones did he make? The answer is 41.

One team in 1962 was asked: By what names are Beethoven’s third, sixth and ninth symphonies known? The answer: Eroica, Pastoral, Choral.

Paxman’s comments were supported by Peter Gwyn, executive producer of University Challenge, who studied the content of the early shows for University Challenge: the First 40 Years.

“Looking at the questions from the 1960s, they were different in style. They were loftier, but they weren’t harder,” he said. “There weren’t many questions on the sciences.

“In 1962, for example, a team struggled to answer the question: ‘Who came up with E=MC squared?’.”

If today’s students were asked questions from the 1960s they would achieve higher scores than they would with contemporary questions, he added, and supplied a list of questions so readers of The Times could decide for themselves.

Humphrys, who also spoke at the festival on Saturday, said Mastermind questions were also more difficult than in the past. When told that Paxman disagreed, he said: “Well, deliver this message to him. He’s welcome to test this proposition by appearing as a guest on Celebrity Mastermind.

“We’ll deliberately make the questions a bit easier for him, if he likes. Alternatively, we could have a shoot-out. I could put to him a set of questions chosen at random from the last ten programmes and he could do the same. Come on, Paxman, if you think you’re hard enough.”

Paxman later described any report of his comments as a “confection of nothing”. It seems, on this basis, that he is unlikely to take up Humphrys’s challenge.

Questions then and now

University Challenge, 1962:

Q: Thursday is named after the god Thor. After whom is Wednesday named?

A: Woden.

Q: Who was the last tsar of Russia?

A: Nicholas II

Q: Solomon Grundy was born on Monday. When did he die?

A: Saturday

University Challenge, 2009:

Q: Lisa, that is, the laser interferometer space antenna, is planned to be the first space-based observatory dedicated to the detection of what disturbance of space-time?

A: Gravity waves

Q: What word did Edmund Spenser use in the The Faerie Queene as an epithet for the thousand-tongued monster born of Cerberus and Chimera, by which he symbolised false accusation? It is now used to mean conspicuous or obvious.

A: Blatant

Q: Which Greek letter links: the temperature point below which liquid helium in equilibrium with its vapour exhibits superfluidity; a moth so named because of the pattern on its wings; and a shield marking of the Ancient Spartan army?

A: Lambda

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