The puzzle - to colour a map using at most four colours - the 4 colour problem.
Key point, no two adjacent regions have the same colour - two regions are adjacent if they share a common boundary segment (not just a point).
That only four colours are needed was the first major theorem proved by a computer! [Done by Appel and Haken].
You select the map and backtracking is used to solve it.
Press Show Solving to see how it does it - using backtracking.
Some maps can be solved using only 3 colours - you can try this.
Press Test Adjacency to see which regions are deemed to be adjacent. Here a Red region shows one region and the green regions those that are considered adjacent.