From A to C
Source: Greek MO 2015
March 22, 2015
combinatorics
Problem Statement
Square with side-length is divided into small (fundamental) squares by drawing lines parallel to its sides (the case is presented on the diagram).The squares' vertices that lie inside (or on the boundary) of the triangle are connected with each other with arcs.Starting from ,we move only upwards or to the right.Each movement takes place on the segments that are defined by the fundamental squares and the arcs of the circles.How many possible roots are there in order to reach ;