This puzzle is a gift

UPDATE: Check out the solution here

By Alex Bellos, Mon 30 Sep 2024, 02:10 EDT, Last modified on Wed 2 Oct 2024, 05:02 EDT

Today’s puzzle has caught the attention of academic mathematicians.

Before we get into the nitty-gritty of calculations, why not take a moment to make an intuitive guess? You might find the answer surprising!

**The 15 Boxes**

In this intriguing game, Andrew and Barbara go head-to-head with a grid of fifteen boxes.

Prizes are hidden in two randomly selected boxes. Andrew will examine the boxes row by row, in the sequence ABCDEFGHIJKLMNO, while Barbara will look at them column by column, following AFKBGLCHMDINEJO.

Each turn, Andrew and Barbara open their respective boxes at the same time—starting with A on the first turn, B with F on the second, C with K on the third, and so on. This raises an intriguing question: Who is more likely to find a prize first?
a) Andrew.
b) Barbara.
c) Both equally likely.

I’ll be back at 5 PM UK time with the solution. Please, no spoilers! In the meantime, feel free to share your thoughts on your favorite boxes.

UPDATE: The solution is available here.

This puzzle was initially introduced (in a slightly different form) by Timothy Chow in 2010, but it has recently sparked lively discussions among prominent mathematicians. Stay tuned for more insights along with the solution.


If I had come across Chow’s puzzle earlier, I might have included it in my latest book, *Think Twice*, a collection of many counter-intuitive conundrums (titled *Puzzle Me Twice* in the US). This book is perfect for solo enjoyment or group discussions, as each puzzle invites lively debate.

*Think Twice: Solve the simple puzzles (almost) everyone gets wrong* (Square Peg, £12.99). To support the *Guardian* and *Observer*, you can order your copy at guardianbookshop.com (delivery charges may apply).

Since 2015, I’ve been curating a puzzle here every other Monday and am always excited to uncover more captivating puzzles. If you have any suggestions, don’t hesitate to reach out!