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# Chapter 22: Map

You are given a map consisting of a number of regions. Your task is to colour each region with one of four colours, in such a way that no two regions sharing a boundary have the same colour. You are provided with some regions already coloured, sufficient to make the remainder of the solution unique.

Only regions which share a length of border are required to be different colours. Two regions which meet at only one point (i.e. are diagonally separated) may be the same colour.

I believe this puzzle is original; I've never seen an implementation of it anywhere else. The concept of a four-colouring puzzle was suggested by Owen Dunn; credit must also go to Nikoli and to Verity Allan for inspiring the train of thought that led to me realising Owen's suggestion was a viable puzzle. Thanks also to Gareth Taylor for many detailed suggestions.

## 22.1 Map controls

To colour a region, click the left mouse button on an existing region of the desired colour and drag that colour into the new region.

(The program will always ensure the starting puzzle has at least one region of each colour, so that this is always possible!)

If you need to clear a region, you can drag from an empty region, or from the puzzle boundary if there are no empty regions left.

Dragging a colour using the right mouse button will stipple the region in that colour, which you can use as a note to yourself that you think the region might be that colour. A region can contain stipples in multiple colours at once. (This is often useful at the harder difficulty levels.)

You can also use the cursor keys to move around the map: the colour of the cursor indicates the position of the colour you would drag (which is not obvious if you're on a region's boundary, since it depends on the direction from which you approached the boundary). Pressing the return key starts a drag of that colour, as above, which you control with the cursor keys; pressing the return key again finishes the drag. The space bar can be used similarly to create a stippled region. Double-pressing the return key (without moving the cursor) will clear the region, as a drag from an empty region does: this is useful with the cursor mode if you have filled the entire map in but need to correct the layout.

If you press L during play, the game will toggle display of a number in each region of the map. This is useful if you want to discuss a particular puzzle instance with a friend – having an unambiguous name for each region is much easier than trying to refer to them all by names such as ‘the one down and right of the brown one on the top border’.

(All the actions described in section 2.1 are also available.)

## 22.2 Map parameters

These parameters are available from the ‘Custom...’ option on the ‘Type’ menu.

Width, Height
  Size of grid in squares.
Regions
  Number of regions in the generated map.
Difficulty
  In ‘Easy’ mode, there should always be at least one region whose colour can be determined trivially. In ‘Normal’ and ‘Hard’ modes, you will have to use increasingly complex logic to deduce the colour of some regions. However, it will always be possible without having to guess or backtrack.

  In ‘Unreasonable’ mode, the program will feel free to generate puzzles which are as hard as it can possibly make them: the only constraint is that they should still have a unique solution. Solving Unreasonable puzzles may require guessing and backtracking.