2
Problems(2)
Restoring coordinate system
Source: Moscow mathematic olympiad 2022, P11.2
9/29/2022
In a Cartesian coordinate system (with the same scale on the x and y axes)there is a graph of the exponential function . Then the y-axis and all marks on the x-axis erased. Only the graph of the function and the x-axis remained without a scale and a mark of .
How can you restore the y-axis using a compass and ruler?
analytic geometryRulercompassgeometry
Volleyball championship
Source: Moscow mathematic olympiad 2022, Day 2 P11.2
9/29/2022
The volleyball championship with teams was held in one round (each team played with each exactly one
times, there are no draws in volleyball). It turned out that some two teams won the same number of matches.
Prove there are the three teams that beat each other in a round robin (i.e. A beat B, B beat C, and C beat A).
combinatorics