Fill every square with a number so that each number appears once in every row, every column and every block marked by thick lines. The game mode gives the blocks’ shape:
Settings add rules, which a board’s name says:
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.
To place a number, click in a square to select it, then type the number on the keyboard. To erase a number, click to select a square and then press Backspace.
Right-click in a square and then type a number to add or remove the number as a pencil mark, indicating numbers that you think might go in that square. 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.
You can also use the arrow keys to move the selected square around. Press Enter to toggle between entering numbers and entering pencil marks, and Backspace or Space to clear a square. On grids of more than 9 numbers, the numbers past 9 are typed as letters.
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. Once every empty square has marks, the press crosses out of each the numbers already placed in its row, column and block, and in its diagonal or cage where the board has them. On a grid of 22 numbers or more, M is the letter for 22, so there only the button fills the marks.
Hint explains the next step rather than simply making it. It works from your own numbers and pencil marks, so it carries on from wherever you are; if a number you’ve entered is wrong, or a cell’s pencil marks have crossed out its answer, it asks you to fix the highlighted mistakes first. It pencils in only as it needs to: a cell with no marks counts as holding every number its row, column and block (and, in X mode, diagonal, and in Killer mode, cage) don’t already hold, and the hint writes a cell’s marks only when its next step crosses one out or reasons from them. Much of a puzzle then needs no marks at all. If you would rather it filled in every cell’s marks first (the same as pressing Fill marks), set Hints pencil in to Every candidate first in the preferences.
A few ideas are worth learning by name:
On the hardest boards that need no guessing, a step may be a wing. Take a cell whose pencil marks are down to two values, say a or b, and two cells it can’t repeat a value with, both outlined: one marked a and c, the other b and c. Whatever goes in the middle cell, one of the outlined cells must have c, so a cell that can’t repeat a value with either of them can’t be c. If the middle cell could be c as well, the same holds for a cell that can’t repeat a value with the middle cell either.
If you’ve turned on the preference that removes a number from the pencil marks it rules out when you place it, the hint leaves that tidying to the placement rather than spelling it out as a step of its own. On an Unreasonable board, deduction can run out before the grid is full; the hint says so rather than guessing.
These parameters are available from the ‘Custom type…’ option on the ‘Type’ menu.