Sudoku Learning Hub
Master every sudoku solving technique, from beginner to expert.
Enough to solve every Easy and Medium puzzle.
Full House
When a row, column, or box has only one empty cell, the missing digit goes there.
Naked Single
When a cell has only one remaining candidate after all eliminations, that candidate is the solution.
Hidden Single
A Hidden Single is a digit that has only one possible cell left in a row, column or box. It must go there, even if that cell still has other candidates.
With these, you can solve every Advanced puzzle.
Pointing Pair
When the only cells in a box that can hold a digit all lie in one row or column, the box's copy of that digit is on that line, so the digit can be crossed out of the rest of the line.
Claiming Pair
When the only cells in a row or column that can hold a digit all lie in one box, the line's copy of that digit is in that box, so the digit can be crossed out of the rest of the box.
Naked Pair
A Naked Pair is two cells in the same house that hold the same two candidates and nothing else. Those two digits must go in those two cells, so you can remove them from every other cell in the house.
Hidden Pair
A Hidden Pair is two digits that fit in only two cells of a house. Those two cells must hold those two digits, so every other candidate in them can go.
Naked Triple
A Naked Triple is three cells in the same house whose candidates, put together, are just three digits. Those three digits must go in those three cells, so you can remove them from every other cell in the house.
Hidden Triple
A Hidden Triple is three digits that fit in only three cells of a house. Those cells must hold those three digits, so every other candidate in them can go.
With these, you can solve 83% of Hard puzzles.
X-Wing
When a candidate appears in exactly two cells in each of two rows, and those cells share the same two columns, the candidate can be eliminated from the other cells in those columns.
Skyscraper
A Skyscraper uses one digit with exactly two possible cells in each of two rows (or two columns). One end of each pair lines up with the other, forming the base; the other ends are the tops. At least one top holds the digit, so it can be removed from cells that see both tops.
Two-String Kite
A Two-String Kite uses one digit with exactly two places in a row and exactly two in a column. One cell of the row pair and a different cell of the column pair share a box, so at least one of the two far ends holds the digit, and any cell that sees both far ends can't.
XY-Wing
An XY-Wing (also called a Y-Wing) uses three bivalue cells — a hinge and two wings — to eliminate a candidate from cells that see both wings.
XYZ-Wing
An XYZ-Wing extends the XY-Wing concept with a trivalue hinge cell (A,B,C) and two bivalue wings — one with (A,C) and one with (B,C). The common digit C can be eliminated from cells that see all three.
W-Wing
A W-Wing joins two cells with the same two candidates through a strong link on one of those digits. It proves that at least one of the two cells holds the other digit, so that digit can go from every cell that sees both.
Unique Rectangle
A Unique Rectangle (Type 1) relies on the puzzle having exactly one solution. Four cells in a rectangle across two boxes, none of them givens, can't all end up holding only the same two digits, or they could be swapped for a second solution. So when three corners hold just that pair, the fourth corner can't be either digit.
Empty Rectangle
An Empty Rectangle uses one digit in a box where every place for it lies on one row and one column of the box, which cross. Together with a strong link outside the box, it removes the digit from one cell.
Finned X-Wing
A Finned X-Wing is an X-Wing with one or two extra candidates, the fin, in one of its rows, inside the box of one corner. The digit still goes from the cells that both the X-Wing and the fin rule out.
With these, you can solve 93% of Hard puzzles and 23% of Expert ones.
Few of our puzzles need these, but they are worth knowing.
Swordfish
The Swordfish extends the X-Wing from two rows and two columns to three rows and three columns, allowing eliminations when a digit's candidates align across three rows.
Naked Quad
A Naked Quad is four cells in one house whose candidates, put together, are only four digits. Those digits must go in those four cells, so they can be removed from every other cell of the house. Naked Quads are rare: this lesson is in the Rarely needed tier.
Hidden Quad
Four digits that, in one house, fit only in the same four cells. Those cells must hold those four digits, so every other candidate can be removed from them. Hidden Quads are rare: this lesson is in the Rarely needed tier.
Jellyfish
A Jellyfish extends the fish pattern family to four rows and four columns. When a candidate digit is restricted to at most four columns across four rows, it can be eliminated from those columns in all other rows.