Any map can be coloured with just four colours so that neighbouring countries are always different — a famous result called the Four Colour Theorem, first proved in 1976 with the help of a computer.
Here a few regions start coloured, and there is exactly one way to finish the map. Regions that share a border, even a short one, must be different; regions that meet only at a corner may match.
Look for a region whose neighbours already show three different colours — it must take the fourth. When that runs out, try a colour and follow what it forces.
Colour every region with one of four colours so that regions sharing a border never match.
The full guide, with a worked example and common mistakes: How to play Four Colours.
Four is always enough for any flat map — that is the Four Colour Theorem. Three is not always enough.
Each colour has a shape (● red, ▲ yellow, ■ green, ◆ blue) so you can tell them apart without colour.
Yes — the starting colours are chosen so there is exactly one way to finish.
Open the Four Colours Solver, draw the regions, add the given colours and press Solve.