5
Part of 2022 May Olympiad
Problems(2)
winning strategy, vertices of regular n-gon
Source: 2022 May Olympiad L2 p5
9/4/2022
The vertices of a regular polygon with sides are marked on the blackboard. Ana and Beto play alternately, Ana begins. Each player, in turn, must do the following:
join two vertices with a segment, without cutting another already marked segment; or
delete a vertex that does not belong to any marked segment.
The player who cannot take any action on his turn loses the game. Determine which of the two players can guarantee victory:
a) if
b) if
combinatoricswinning strategy
isosceles triangles cut into 3 triangles, 2/3 isosceles, 2022 May Olympiad L1 P5
Source:
9/4/2022
Vero had an isosceles triangle made of paper. Using scissors, he divided it into three smaller triangles and painted them blue, red and green. Having done so, he observed that:
with the blue triangle and the red triangle an isosceles triangle can be formed,
with the blue triangle and the green triangle an isosceles triangle can be formed,
with the red triangle and the green triangle an isosceles triangle can be formed.
Show what Vero's triangle looked like and how he might have made the cuts to make this situation be possible.
geometryisosceles