game with blue and red dots, special points
Source: 1998 Estonia National Olympiad Final Round grade 10 p5
March 14, 2020
combinatoricsColoring
Problem Statement
The paper is marked with the finite number of blue and red dots and some these points are connected by lines. Let's name a point special if more than half of the points connected with has a color other than point . Juku selects one special point and reverses its color. Then Juku selects a new special point and changes its color, etc. Prove that by a finite number of integers Juku ends up in a situation where the paper has not made a special point.