MathDB

2

Part of 2017 May Olympiad

Problems(2)

Olimpiada de Mayo(OMA) 2017

Source: May Olympiad(Olimpiada de Mayo) 2017

10/2/2017
Alice writes differents real numbers in the board, if a,b,ca,b,c are three numbers in this board, least one of this numbers a+b,b+c,a+ca + b, b + c, a + c also is a number in the board. What's the largest quantity of numbers written in the board???
algebra
paint 33 squares on a 9x9 board 2017 May Olympiad L1 p2

Source:

8/25/2021
Is it possible to paint 3333 squares on a 9×99\times 9 game board, so that each row and each column of the board has a maximum of 44 painted squares, but if we also paint any other square a row or column appears that has 55 squares painted?
combinatorics