14

Part of 2013 Iran Team Selection Test

Problems(1)

4n Right Angles

Source: Iran TST 3, Day 1, Problem 2

n

rectangles in the plane. Prove that between

4n

right angles formed by these rectangles there are at least

[4\sqrt n]

distinct right angles.

geometryrectangleanalytic geometryinductioncombinatorics proposedcombinatorics