All roads lead to the same place

Avraham Trakhtman, a mathematician who worked as a security guard, recently succeeded in solving something called the Road Colouring Problem:

[This] was first posed in 1970 by Benjamin Weiss, an Israeli-American mathematician, and a colleague, Roy Adler... Weiss said he believed that given a finite number of roads, one should be able to draw up a map, coded in various colors, that would lead to a certain destination regardless of the point of origin.

If you haven't fully grasped it, maybe this will help. (Thanks: E.)