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UKMT Pink Kangaroo, 2025

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Patrick numbers certain squares on a sheet of grid paper. Each square has a side-length of $0.5\text{ cm}$ . He starts by putting 1 in one of the squares and then numbers $2, 3, 4, 5, \ldots$ in squares in an anti-clockwise direction, as shown. He stops when he has numbered 2025 squares, and looks at the figure made up of all numbered squares. What is the perimeter of this figure?

(A) $80\text{ cm}$ (B) $90\text{ cm}$ (C) $120\text{ cm}$ (D) $180\text{ cm}$ (E) $360\text{ cm}$

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