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Earlier today I set you the following puzzle, which has been doing the rounds in the academic community, because of its counter-intuitive result. Here it is again with the solution.

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?

Intuitively, it feels like both players should get to the box at the same time. If the prizes are in randomly-chosen boxes, why should one search method have an advantage over another?

Indeed, if there was only a single prize in a single box, that would be the answer: they would be equally likely to win. What changes everything is that that there are two prizes, and the game is over when the first of them is found.

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