MathDB

1

Part of 2022 May Olympiad

Problems(2)

red squares in a 7x7 board

Source: 2022 May Olympiad L2 p1

9/4/2022
In a 7×77\times7 board, some squares are painted red. Let aa be the number of rows that have an odd number of red squares and let bb be the number of columns that have an odd number of red squares. Find all possible values of a+ba+b. For each value found, give a example of how the board can be painted.
Coloringcombinatorics
wrong clock

Source: 2022 May Olympiad L1 p1

9/5/2022
This morning, Emi dropped the watch and from there it started to move more slowly. When, according to the clock, 22 minutes have passed, in reality it has already been 33. Now it is 6:256:25 pm and the clock says it is 3:303:30 pm. What time did Emi drop the watch?
algebra