olymmath

OPM 2003

Portuguese Mathematical Olympiad 2003.

Official paper

The official paper in 2 languages

Portuguese (day1) · Portuguese (day2)

Final day 1

Problem 3

  • Final day 1

Raquel painted 650650 points in a circle with a radius of 1616 cm. Shows that there is a circular crown with 22 cm of inner radius and 33 cm of outer radius that contain at least 1010 of these points.

Answer, solutions and source

Final day 2