Think Twice

Chalkdust

18 February 2025

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Alex Bellos is a journalist and broadcaster who writes a fortnightly column of mathematical puzzles for the Guardian. Think Twice (Penguin, Waterstones) is his latest book all about the puzzles that most of us get wrong.

Style

Think Twice contains 70 puzzles, each designed to make you get the answer wrong, then think about why that was. With a subtitle like Solve the Simple Puzzles (Almost) Everyone Gets Wrong, this should come as no surprise. The book includes not just the puzzles, which are really enjoyable, but also the explanations of how to solve them and why many people get them wrong.

Control

The puzzles have been taken from a variety of sources, all with the intention of highlighting when our intuition goes wrong. With some of the puzzles, the story around where they come from and how they have been used to study people’s problem solving, is just as interesting as the puzzles themselves. One observation is that the problem Baffling Bloodlines contains an amusing typo. This problem asks what proportion of the current UK population are descendants of Edward III, and in the solution says that $0.995\times 10^{32 768}=4.64^{-72}$ is a tiny number, of course on the right hand side this should be $0.995^{32768}$. This typo was in the original Waterstones blog article discussing the problem which the book cites, so I like to view this as a fun easter egg to check that everyone is paying attention when reading the solutions.

Damage

With puzzle books there is always the danger that you have seen some of the puzzles before. However, with Think Twice , this is actually a good thing. The emphasis of the book is that sometimes you need to see a puzzles twice to understand both how to solve it and why your first attempt was wrong. This means that going through the puzzles that you have seen before is just as valuable as trying those that a totally new to you.

Aggression

I loved this book, and got as much joy sharing the puzzles with friends and family as I did trying to solve them myself. This is a great book for anyone who enjoys solving puzzles, sharing puzzles, getting puzzles wrong, and the aha moment when you understand why you got it wrong.

You can vote for your favourite book on the Book of the Year shortlist below. The winning book will be crowned the Chalkdust Readers’ Choice. Voting closes at midday (GMT) on Wednesday 26 February 2024.

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