2
Part of 2022 Bundeswettbewerb Mathematik
Problems(2)
Counting triangles in triangles…
Source: Bundeswettbewerb Mathematik 2022 Round 1 P2
3/30/2022
Eva draws an equilateral triangle and its altitudes. In a first step she draws the center triangle of the equilateral triangle, in a second step the center triangle of this center triangle and so on.
After each step Eva counts all triangles whose sides lie completely on drawn lines. What is the minimum number of center triangles she must have drawn so that the figure contains more than 2022 such triangles?
combinatoricscombinatorial geometryTriangleGermany
A dice game
Source: German Bundeswettbewerb 2022, Round 2, Problem 2
9/14/2022
On a table lie 2022 matches and a regular dice that has the number on top. Now Max and Moritz play the following game:
Alternately, they take away matches according to the following rule, where Max begins: The player to make a move rolls the dice over one of its edges and then takes a way as many matches as the top number shows. The player that cannot make legal move after some number of moves loses.
For which can Moritz force Max to lose?
combinatorics