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MathNet 2024-part-02 — 168 problems (EN–VI) Question 27

Math Olympiad Vault · MathNet 2024-part-02 — 168 problems (EN–VI)

Question 27

Kadi has a square pasture with a side length of $2$, where a goat lives. Since there is no fence around the pasture, Kadi fears that the goat might run away at any moment. Instead of getting a fence, Kadi decided that it would be cheaper to place scarecrows around the pasture, which the goat is afraid of. It is known that the goat will not dare to be at a distance of $1$ or less from any scarecrow. Find the minimum number of scarecrows that Kadi needs to confine the goat to a finite area that entirely contains the area within the boundaries of the pasture.