5
Problems(2)
acute triangle from partitions of diagonals of 2017-gon (2016 Auckland MO J5)
Source:
11/13/2021
A regular -gon is partitioned into triangles by a set of non-intersecting diagonals.
Prove that among those triangles only one is acute-angled.
combinatorial geometryacuteregular polygon
streets avenues and crescents in a city (2016 Auckland MO S5)
Source:
11/13/2021
In a city at every square exactly three roads meet, one is called street, one is an avenue, and one is a crescent. Most roads connect squares but three roads go outside of the city. Prove that among the roads going out of the city one is a street, one is an avenue and one is a crescent.
combinatorics