OPM 2018

Portuguese Mathematical Olympiad 2018.

Official paper

The official paper in 2 languages

Portuguese (day1) · Portuguese (day2)

Final day 1

Problem 1

Final day 1

Answer, solutions and source

Problem 2

Final day 1

Answer, solutions and source

Problem 3

Final day 1

How many ways are there to paint an $m \times n$ board, so that each square is painted blue, white, brown or gold, and in each $2 \times 2$ square there is one square of each color?

Answer, solutions and source

Final day 2

Problem 4

Final day 2

Answer, solutions and source

Problem 5

Final day 2

Answer, solutions and source

Problem 6

Final day 2

Answer, solutions and source