MathDB

2

Part of 2016 May Olympiad

Problems(2)

2x2 squares in 5x5 board May Olympiad (Olimpiada de Mayo) 2016 L2 P2

Source:

9/25/2021
How many squares must be painted at least on a 5×55 \times 5 board such that in each row, in each column and in each 2×22 \times 2 square is there at least one square painted?
combinatorics
In a sports competition

Source: May Olympiad 2016 L1 P2

3/14/2021
In a sports competition in which several tests are carried out, only the three athletes A,B,CA, B, C. In each event, the winner receives xx points, the second receives yy points, and the third receives zz points. There are no ties, and the numbers x,y,zx, y, z are distinct positive integers with xx greater than yy, and yy greater than zz. At the end of the competition it turns out that AA has accumulated 2020 points, BB has accumulated 1010 points and CC has accumulated 99 points. We know that athlete AA was second in the 100-meter event. Determine which of the three athletes he was second in the jumping event.
number theorycombinatorics