Today’s puzzle has recently got attention among academic mathematicians.
Make an intuitive guess at the answer before you try to work it out – the answer is very surprising.
The 15 boxes
Andrew and Barbara are playing a game, in which fifteen boxes are arranged in a grid as shown below.
Prizes are put in two randomly-chosen boxes. Andrew will search the boxes row by row, so his search order is ABCDEFGHIJKLMNO. Barbara will search column by column, so her order is AFKBGLCHMDINEJO.
If Andrew and Barbara open their boxes together each turn, that is, on the first turn, they both open A, on the second, Andrew opens B and Barbara opens F, on the third Andrew opens C, and Barbara opens K, and so on, who is more likely to find a prize first?
a) Andrew.
b) Barbara.
c) Both equally likely.
I’ll be back at 5pm UK with the solution. PLEASE NO SPOILERS. Instead discuss your favourite boxes.
The puzzle was first posed (in a slightly different form) by Timothy Chow in 2010, but it and similar problems have recently been the subject of discussions by prominent mathematicians. More of this with the solution.
Had I known about Chow’s puzzle, I might have included it in my latest book, Think Twice, a compilation of many counter-intuitive conundrums. (In the US it is called Puzzle Me Twice.) The idea behind the book is for it to be read on its own, or in a group, as these puzzles are great fun to be argued over.
Think Twice: Solve the simple puzzles (almost) everyone gets wrong (Square Peg, ££12.99). To support the Guardian and Observer, order your copy at guardianbookshop.com. Delivery charges may apply.
I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.