Today’s puzzle has recently received attention among academic mathematicians.
Make an intuitive guess about the answer before trying 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 placed 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 open, 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. Book your favorite boxes instead.
The puzzle was first posed (in a slightly different form) by Timothy Chow in 2010, but this and similar problems have recently been the subject of discussion 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 counterintuitive puzzles. (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 reason about.
Think Twice: Solve the Simple Riddles (Almost) Everyone Gets Wrong (Square Peg, ££12.99). To support the Guardian and Observer, order your copy from guardianbookshop.com. Delivery charges may apply.
I’ve been doing a puzzle here on alternate Mondays since 2015. I’m always on the lookout for great puzzles. If you want to suggest one, email me.
