TOT 109 1986 Spring J3 strees of a town arranged in 3 directions, equilateral
Source:
August 29, 2019
combinatoricscombinatorial geometry
Problem Statement
The streets of a town are arranged in three directions , dividing the town into blocks which are equilateral triangles of equal area. Traffic , when reaching an intersection, may only go straight ahead, or turn left or right through , as shown in the diagram.
https://cdn.artofproblemsolving.com/attachments/3/6/a100a5c39bf15116582bc0bceb76fcbae28af9.png
No turns are permitted except the ones at intersections . One car departs for a certain nearby intersection and when it reaches it a second car starts moving toward it. From then on both cars continue travelling at the same speed (but do not necessarily take the same turns). Is it possible that there will be a time when they will encounter each other somewhere?( N . N . Konstantinov , Moscow )