Is the three-door problem a bit of a cliché? When Ionica Smeets and Jan Beuving get stuck into it, it’s still great fun even after 99 times.

‘Do you know the three-door problem from probability theory?’ In some circles, people at parties will start looking around bored as soon as this question is asked. Among mathematicians in particular, it’s considered a hackneyed topic. Of course they know this puzzle, which is based on a segment from an American television quiz show that was later copied in the Netherlands on the Willem Ruisshow.

Chances doubled

In this part of the quiz, there are three doors: behind one of them is a car, and behind the other two is a goat. The contestant chooses a door behind which their prize is hidden, hoping it’s a car. The quizmaster then opens one of the other two doors, from behind which a surprised goat emerges. The quizmaster then offers the player the chance to switch doors. But is that a wise move, or not, or does it make no difference?

The latter, intuition suggests, but according to probability theory, the player is actually better off choosing the other door. After all, when they made their initial choice, the probability of a car was only one in three, whilst the probability of a goat was as high as two in three. Switching doubles the chance of success!

Imagination

Jan Beuving and Ionica Smeets take this Monty Hall problem – named after the quizmaster who presented the American quiz show – as the starting point for their book *The Car, the Goat and the Maths*. Contrary to what the title might suggest, the book does not focus on mathematics but on language and the power of imagination.

Beuving is a mathematician, songwriter and comedian; Smeets is a mathematician, professor of science communication at Leiden University and a columnist for *de Volkskrant*. They drew inspiration for this book from the literary movement Oulipo, an acronym for *Ouvroir de littérature potentielle* (Workshop for Potential Literature).

This movement imposes strict mathematical or logical rules on its practitioners. A well-known Dutch Oulipo writer was Hugo Brandt Corstius, a magician with language, who, amongst other things, devised sentences in which reading from front to back yielded exactly the same text as reading from back to front. But Drs. P., who composed his songs according to a rhyme scheme set in stone, could also be described as a mathematician with language.

99 times

Following in the footsteps of the French Oulipo writer Raymond Queneau, who in 1947, in the book *Exercises de style*, retold a dull little story 99 times in all sorts of different forms – for example, in telegram style, with as much alliteration as possible, in a single sentence, or as dialogue – Beuving and Smeets wrote 99 pieces in different styles, all based on the goat problem. The Monty Hall problem is not described over and over again, but it does crop up in one way or another in every contribution.

Sometimes funny, sometimes moving

Some of the stories are literary, others are mathematical or written according to formal protocols. The variations lie not only in structure and language, but also in perspectives and associations. Beuving himself admits in one of the stories that, whilst he understands the logic behind the solution to the three-door problem, he actually cannot quite bring himself to believe that it is correct. Two doors, a goat and a car – what difference does it really make which one you choose?

There is a story about other opportunities in life, which are sometimes small but nevertheless strike to give fate a sad twist. There are new riddles, a decision tree appears, and there is a chapter in the style of the aforementioned Drs. P.

All the stories are playful, and many are particularly witty – describing the latter here would be a spoiler, so I shan’t do that. But rest assured that, despite the car and the goats that everyone is by now familiar with, the book is not boring but engaging, funny and sometimes even moving – you can leave that to Beuving and Smeets.

So, are you having a party soon? You’re sure to make a splash by asking, ‘Have you heard of the book about the car, the goat and maths?’ Even if there are lots of mathematicians there.

Opening image: Depositphotos