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A map colouring logic puzzle. A square map is split into about twenty regions; colour each one red, yellow, blue or green so that no two regions sharing an edge match. A few regions are given, every puzzle is new, and each has exactly one solution you can reach without guessing.
Pick one of the four colours at the bottom, then tap any square of a region to paint the whole region. Two regions that share an edge must never have the same colour; regions that only touch at a corner do not count as neighbours. Colour every region and the puzzle is solved.
The map is a 10×10 grid split into 18 to 22 regions, outlined with thick light borders. A few regions are already coloured and marked with a white pin — those are the clues, and they cannot be changed. Every other region starts dark.
Each colour also has its own pattern, so you can tell them apart even if some colours look alike to you: red is plain, yellow has diagonal stripes, blue has dots, and green has a grid. Tapping a region again with the colour it already has clears it, and the ✕ button turns your taps into an eraser. Undo takes back your last change, as many times as you like.
If two touching regions end up with the same colour, both are outlined in red and the line under the map says so. Otherwise it counts how many regions are still uncoloured. Every puzzle is generated fresh and checked to have exactly one solution that can be found step by step without guessing.
The clock starts when you press Start and keeps running if you switch away; your score is the time it took, and lower is better. Save a good time to the Hall of Fame from the result card. On a keyboard, keys 1 to 4 pick a colour, 0 or X picks the eraser, and U undoes.
Start where the clues crowd together. A region that touches three differently coloured clues has only one colour left, so it is decided at once — and every region you fill can decide its own neighbours in turn. Scan the map for any region whose given neighbours already use three colours, fill it, and repeat; on many puzzles that alone carries you a long way.
When no region is forced outright, look for pairs. If two neighbouring regions can each only be, say, blue or green, then one of them is blue and the other green, even before you know which is which. That means any third region touching both of them cannot be blue or green — and if it also touches a red clue, it must be yellow. Every puzzle here can be finished with these two ideas alone: crossing out the colours your neighbours already use, and spotting two touching regions that share the same two possibilities.
Big regions are your best friends. A region that touches many others is constrained from every side, so it usually becomes forced early, and once it is coloured it removes that colour from a lot of the map. Small regions tucked between two large ones are often the last to fall. If you get stuck, find the uncoloured region with the most coloured neighbours and count again.
The four colour theorem says that four colours are always enough for any flat map, however complicated, as long as neighbours are regions that share a border rather than a single point. It was first conjectured in 1852 and only proved in 1976 by Kenneth Appel and Wolfgang Haken, with the help of a computer — one of the first major theorems proved that way. These maps are small, but every one of them has been chosen so that the four colours fit together in exactly one way.