<p>You are playing a game. A <img alt="$2 \times 1$" height="12" src="https://latex.artofproblemsolving.com/4/e/0/4e03b602154bf17643e7945df4dae9dcd3a22081.png" width="39" /> rectangle covers two adjacent squares (oriented either horizontally or vertically) of a <img alt="$3 \times 3$" height="15" src="https://latex.artofproblemsolving.com/d/2/7/d278803d72fcc493afb1559174a483aa7f41d143.png" width="42" /> 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?</p>

Question No: 415

You are playing a game. A $2 \times 1$ rectangle covers two adjacent squares (oriented either horizontally or vertically) of a $3 \times 3$ 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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Tags: Combinatorics

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