8

Part of 2015 Tuymaada Olympiad

Problems(2)

Plane with parallelogramms

Source: Tuymaada 2015, Day 2, Problem 8, Senior League

\frac{k(k+1)}{2}+1

points on the planes, some are connected by disjoint segments ( also point can not lies on segment, that connects two other points). It is true, that plane is divided to some parallelograms and one infinite region. What maximum number of segments can be drawn ?
A.Kupavski, A. Polyanski

combinatoricsgeometryparallelogram

Interesting problem

Source: Tuymaada 2015, Day 1, Problem 8, Junior League

Four sages stand around a non-transparent baobab. Each of the sages wears red, blue, or green hat. A sage sees only his two neighbors. Each of them at the same time must make a guess about the color of his hat. If at least one sage guesses correctly, the sages win. They could consult before the game started. How should they act to win?

Tuymaadalogiccombinatorics