MathDB

6

Part of 2014 Saint Petersburg Mathematical Olympiad

Problems(2)

Childs in cells

Source: St Petersburg Olympiad 2014, Grade 11, P6

10/24/2017
In the n×nn \times n table in every cell there is one child. Every child looks in neigbour cell. So every child sees ear or back of the head of neighbour. What is minimal number children, that see ear ?
combinatorics
Some geometry

Source: St Petersburg Olympiad 2014, Grade 9, P6

10/27/2017
Points A,BA,B are on circle ω\omega. Points CC and DD are moved on the arc ABAB, such that CDCD has constant length. I1,I2I_1,I_2 - incenters of ABCABC and ABDABD. Prove that line I1I2I_1I_2 is tangent to some fixed circle.
geometryincenter