3
Part of 2011 Bundeswettbewerb Mathematik
Problems(2)
convex pentagon with each diagonal an angle trisector, is it regular?
Source: Germany Federal - Bundeswettbewerb Mathematik 2011, round 1, p3
4/10/2020
The diagonals of a convex pentagon divide each of its interior angles into three equal parts.
Does it follow that the pentagon is regular?
pentagongeometryconvexdiagonalstrisectordiagonal
prove that all teams play the same number of games.
Source: Germany Federal - Bundeswettbewerb Mathematik 2011, round 2, p3
4/15/2020
When preparing for a competition with more than two participating teams two of them play against each other at most once. When looking at the game plan it turns out:
(1) If two teams play against each other, there are no more team playing against both of them.
(2) If two teams do not play against each other, then there is always exactly two other teams playing against them both.
Prove that all teams play the same number of games.
combinatorics