AMC 10 Step by Step
2023 AMC 10BProblem 10P1-10~4 minPrint

You are playing a game. A 22 ×\times 11 rectangle covers two adjacent squares (oriented either horizontally or vertically) of a 33 ×\times 33 grid of squares, but you are not told which two squares are covered. Your goal is to find at least one square that is covered by the rectangle. A "turn" consists of you guessing a square, after which you are told whether that square is covered by the hidden rectangle. What is the minimum number of turns you need to ensure that at least one of your guessed squares is covered by the rectangle?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.