Color the map with four colors, so that no two adjacent regions have the same color. (Regions touching at only one corner do not count as adjacent.) There is a unique coloring consistent with the colored regions you are already given.
On a touch screen, a tap does what a click does, and a long press what a right-click does (more ways to right-click). A key the puzzle’s controls show as a button can be pressed there instead of on a keyboard.
Drag from a colored region to a blank one to color the latter the same color as the former. Drag from outside the grid into a region to erase its color. (You cannot change the colors of the regions you are given at the start of the game.)
Or tap a region to select it and press one of the four color buttons below the grid, which is the same thing without the drag — each button is painted in the color it fills with, and the digit on it is the key that does the same from the keyboard. The Clear button empties the selected region.
Right-drag from a colored region to a blank one to add dots marking the latter region as possibly the same color as the former, or to remove those dots again. Pressing the Marks button below the grid makes ordinary drags — and the color buttons — leave those dots instead of coloring, until you press it again. A right-click without a drag does the same as the Marks button and selects the region, as it does in the other note-taking puzzles. Pencil mode is sticky: once a right-click switches it on, it stays on wherever you click, until you right-click again. The Marks key is lit while it is on, and pressing the key also switches it. To have it last only until your next click, turn off Right-click toggles a sticky pencil mode (stays on until right-clicked again) in the preferences.
Press Fill marks among the puzzle’s controls to write in every pencil mark wherever nothing is placed and no mark is written yet. The M key does the same, on any board where M is not something you type. Marks you have narrowed are left alone, and pressing again never starts over: see Filling in all the pencil marks. Here that dots all four colors into every blank region that has no dots yet. Once every blank region has dots, the press removes from each the dots of colors its neighbors already show.
A region’s dots are the colors it might still be, so Check treats a set of dots that leaves out the region’s real color as a mistake, just as it does a wrong color. A region with no dots is simply unmarked.
The selected region is outlined in green inside its border; while the buttons leave dots, a small green triangle also sits in its top-left corner.
The keyboard can also be used. Move the cursor with the arrow keys, then press a color’s digit to fill the region the cursor is on, or Backspace to empty it. Enter picks up the color under the cursor and a second Enter drops it where you have moved to; pressing Enter twice without moving erases instead, on a region you have colored. Space drops what you are carrying as a dot rather than as a color.
Hint explains the next step rather than simply making it. It reads dots the same way Check does: what a blank region can be comes from its dots, or from all four colors when it has none, less the colors its neighbors already show. It places dots itself only when a deduction rules out a color no neighbor shows, so a map you have never dotted stays undotted until a step needs it. If you would rather the hint start from a fully dotted map, set Hints pencil in to Every candidate first in the preferences: it then begins by pressing Fill all pencil marks twice, just as you would.
The hint names colors by their words, pink, yellow, teal and violet. On a dark board the pink is drawn as a maroon and the yellow as a brown, and the hint calls them that. A step ends by saying what to do: color the region, dot the colors it can still be, or remove the dots it can’t.
The ideas it teaches, from the plainest up:
Every hint is a deduction you could have made from what is on the board. On an Unreasonable board there may come a point where no deduction is left and the only way on is to try something and see whether it works — that is what the difficulty name means. The hint says so rather than guessing for you: save your position, try it, and undo if it breaks.
A hint is refused while a color or a set of dots on the board contradicts the solution; those regions light up instead, exactly as they do for Check & save.
These parameters are available from the ‘Custom type…’ option on the ‘Type’ menu.