Sudoku Strategies

The three techniques you need for every easy puzzle and most medium ones.

• Naked SinglesA naked single is a cell where only one digit from 1 to 9 fits, because the other eight already appear in its row, column or 3x3 box.
• Hidden SinglesA hidden single is a digit that can be placed in only one cell within a row, column or 3x3 box, even though that cell may still have other candidates.
• Pencil MarksPencil marks are small candidate digits written in an empty cell to track which numbers can still go there.

Pair and reduction techniques that crack hard puzzles.

• Naked PairsA naked pair is two cells in the same row, column or 3x3 box that contain exactly the same two candidate digits.
• Hidden PairsA hidden pair is two digits whose candidate locations within a row, column or 3x3 box are confined to the same two cells.
• Naked TriplesA naked triple is three cells in the same row, column or box whose combined candidates are exactly three digits.
• Hidden TriplesA hidden triple is three digits whose candidate locations within a row, column or box are confined to the same three cells.
• Pointing PairsA pointing pair occurs when all the candidate cells for a digit within a 3x3 box lie in the same row or column.
• Box-Line ReductionBox-line reduction is the mirror of pointing pairs.

Chain logic and uniqueness arguments for expert and evil puzzles.

• X-WingAn X-wing is a pattern where a digit appears as a candidate in exactly two cells of two different rows, and those four cells line up across the same two columns.
• SwordfishA swordfish is the three-row generalisation of X-wing.
• JellyfishA jellyfish is the four-row generalisation of X-wing (and swordfish).
• XY-WingAn XY-wing is a three-cell pattern.
• XYZ-WingAn XYZ-wing extends XY-wing.
• ColoringColoring is a single-digit chain technique.
• Forcing ChainsA forcing chain picks a cell with two candidates, assumes each candidate in turn, and follows the deductions.
• Unique RectangleA unique rectangle is a four-cell pattern at the corners of a rectangle, spanning exactly two boxes, where three corners have the same two candidates {X, Y}.
• BUG (Bivalue Universal Grave)A BUG (bivalue universal grave) pattern arises when every empty cell in the grid would have exactly two candidates.
• NishioNishio picks a single candidate, tentatively places it, and follows forced deductions until either a contradiction or a valid completion appears.