Brainteaser: solve Alex Bellos’ bookish puzzle

Challenge yourself with a book-themed brainteaser from Alex Bellos, The Guardian’s resident puzzle columnist.

Think Twice – Bellos' new book – is a collection of 70 intriguing puzzles, each deceptively simple on the surface, but guaranteed to challenge and confound. These are puzzles to get stuck into, and getting them wrong is all part of the fun (especially with Alex’s simple explanations on hand to help you understand where you went so wrong...).

Ready to take on one of Alex’s puzzles? Below, he has devised a fiendish book-themed brain-teaser. Introducing the Bemusing Bookclub…

Puzzle: The Bemusing Bookclub

In a bookclub, everyone enjoys either Thrillers or Comedies, or they enjoy both.

If exactly 70 per cent enjoy Thrillers and exactly 60 per cent enjoy Comedies, what percentage enjoy both?

a) 30

b) 40

c) 60

Ready to see if you got the answer right? Don't scroll any further until you are...

Answer:

30 per cent enjoy both Thrillers and Comedies.

Des MacHale, Emeritus Professor of Maths at University College Cork, says very few people get this question right because solving it requires the use of a Venn diagram, and this method of logical deduction is not often taught in schools.

Once you draw a Venn diagram, it fills in easily.

If 70 per cent enjoy Thrillers, then 30 per cent only enjoy Comedies. And if 60 per cent enjoy Comedies, then 40 per cent only enjoy Thrillers. Once 30 and 40 are placed in the correct regions of the diagram, the intersection containing book group members who enjoy both types of books must be 30 per cent.