MathDB

Bosnia and Herzegovina 2018 TST Day 1 Problem 3

Source: Bosnia and Herzegovina 2018 TST

September 15, 2018

combinatoricspolygonrotationgeometrygeometric transformation

Problem Statement

Find all values of positive integers

a

and

b

such that it is possible to put

a

ones and

b

zeros in every of vertices in polygon with

a+b

sides so it is possible to rotate numbers in those vertices with respect to primary position and after rotation one neighboring

0

and

1

switch places and in every other vertices other than those two numbers remain the same.