The map of a town shows a plane divided into equal equilateral triangles. The sides of these triangles are streets and their vertices are intersections; 6 streets meet at each junction. Two cars start simultaneously in the same direction and at the same speed from points A and B situated on the same street (the same side of a triangle). After any intersection an admissible route for each car is either to proceed in its initial direction or turn through 120o to the right or to the left. Can these cars meet? (Either prove that these cars won’t meet or describe a route by which they will meet.)
https://cdn.artofproblemsolving.com/attachments/2/d/2c934bcd0c7fc3d9dca9cee0b6f015076abbdb.png geometryEquilateralcombinatoricscombinatorial geometry