3
Part of 2018 May Olympiad
Problems(2)
Liars and knights
Source: May Olympiad(Olimpiada de mayo) 2018
10/8/2018
The inhabitants of a city are divided in two groups: the knights(only speak the truth) and the liars(only speak the lie). The inhabitants sat in a circle and everybody spoke "My two neighbours(in the left and in the right) are liars". After this, one inhabitant got off the circle. The inhabitants sat again in a circle(not necessarily in the same order), and everybody spoke "None of my two neighbours(in the left and in the right) is of the same group of myself"
Can we determine the group of the inhabitant that got off the city?
combinatorics
computational geometry for 13yo, segment inside a regular 10-gon
Source: May Olympiad (Olimpiada de Mayo) 2018 L1
9/10/2018
Let be a regular -sided polygon that has all its vertices in one circle with center and radius . The diagonals and intersect at and the diagonals and intersect at . Calculate the measure of the segment .
geometryComputationalpolygon