Problem 20 · 2025 Math Kangaroo
Hard
Geometry & Measurement
spiral-patternperimeter
Daniel numbers some squares on a piece of squared paper. He starts with a random square and numbers the squares 1, 2, 3, 4, 5, …, 2025 anti-clockwise (see illustration). At the end he considers the figure that results from all 2025 numbered squares. Each square has a side length of 0.5 cm. What is the perimeter of the figure?
Show answer
Answer: D — 90 cm
Show hints
Hint 1 of 2
The numbered squares form a growing spiral; you only need its outline, not every cell.
Still stuck? Show hint 2 →
Hint 2 of 2
Find the bounding rectangle the spiral fills and account for the small notch where it ends.
Show solution
Approach: bound the spiral and read off the perimeter
- Numbering 1..2025 in an outward spiral fills an almost-square block of cells.
- 2025 = 45², so the spiral exactly fills a 45×45 square of cells.
- Side = 45×0.5 = 22.5 cm; perimeter = 4×22.5 = 90 cm.
Mark:
· log in to save