Kerf Puzzle

Sudoku solving techniques

Every Sudoku on this site can be solved with the techniques below, one logical step at a time and without guessing. They run from the easiest to the hardest, and a puzzle's level is set by the hardest one it needs. The hint button in the game shows these same steps.

Naked single

Used in: Easy, Medium, Hard, Expert

Pick an empty cell and look at its row, its column and its box. If eight different digits already appear there, only the ninth can go in the cell.

Example

Hidden single

Used in: Easy, Medium, Hard, Expert

Pick a row, a column or a box and one digit it is still missing. Check each empty cell there, and rule it out if the digit already sits in that cell's row, column or box. When only one cell is left, the digit goes there, even if that cell could hold other digits too.

Example

Locked candidates

Used in: Medium, Hard, Expert

Sometimes a digit's place in a box is not known yet, but every spot left for it lies in the same row or column. That line then gets its digit from this box, so the digit can be crossed off everywhere else in the line. It works the other way round too, from a line into a box. Pencil marks make this easy to see.

Example

Naked pair

Used in: Hard, Expert

If two cells in the same row, column or box can each hold only the same two digits, those two digits must go into those two cells, in some order. Cross both digits off the other cells of that row, column or box.

Example

Hidden pair

Used in: Hard, Expert

If two digits can only go into the same two cells of a row, column or box, those cells must hold those two digits. Every other pencil mark in the two cells can go.

Example

Naked triple

Used in: Hard, Expert

The pair idea grows to three. If three cells in a row, column or box can only hold digits from the same three, those three digits are used up by them, even when each cell shows just two of the three. Cross the three digits off the rest of that row, column or box.

Example

X-Wing

Used in: Expert

Look at one digit in two rows. If it fits in exactly two cells of each row, and those cells sit in the same two columns, the digit takes one corner of that rectangle in each row. Either way both columns get their digit from these two rows, so it can be crossed off everywhere else in those columns. It works with rows and columns swapped too.

Example

XY-Wing

Used in: Expert

Find a cell with exactly two candidates, x and y. Then find two cells it sees, one holding x or z and the other y or z. If the first cell is x, one of them must be z; if it is y, the other must be z. Either way one of them holds z, so a cell that sees both of them can't hold z.

Example

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