How to Solve Sudoku: Learn the Techniques Step by Step

Sudoku Rules: How to Play Sudoku

Techniques for Beginner puzzles

1. Step 1
   Hidden Single (only one place for it)

   When a digit has only one possible cell in a row, column, or box, that cell must be that digit.

Techniques for Easy puzzles

1. Step 2
   Naked Single (only one number fits)

   When a cell has only one candidate left after crossing out the digits in its row, column, and box, that candidate is its answer.

Techniques for Medium puzzles

1. Step 3
   Pointing Pair (lined up inside a box)

   When all of a digit's candidates inside a box lie in one row or column, you can remove that digit from the rest of that row or column outside the box.

2. Step 4
   Box/Line Reduction (a line decides the box)

   When all of a digit's candidates in a row or column lie inside one box, you can remove that digit from the other cells of that box.

Techniques for Hard puzzles

1. Step 5
   Naked Pair

   When two cells in the same row, column, or box have the same two candidates and nothing else, you can remove those two digits from every other cell in that group.

2. Step 6
   Hidden Pair

   When two digits can only go in the same two cells of a row, column, or box, you can remove all other candidates from those two cells.

3. Step 7
   Naked Triple

   When three cells in a group have only three different candidates between them, you can remove those three digits from the other cells of that group.

4. Step 8
   Hidden Triple

   When three digits can only go in the same three cells of a group, you can remove all other candidates from those three cells.

Techniques for Expert puzzles

1. Step 9
   X-Wing

   When a digit has exactly two possible cells in each of two rows, and those cells line up in the same two columns, you can remove that digit from the other cells of those two columns (and the same works with rows and columns swapped).

2. Step 10
   Swordfish

   The three-line version of X-Wing: when a digit's candidates in three rows all fall within the same three columns, you can remove that digit from the other cells of those columns.

3. Step 11
   XY-Wing

   Three cells with two candidates each — a pivot XY and two pincers XZ and YZ that each see the pivot — let you remove Z from any cell that sees both pincers.

4. Step 12
   XYZ-Wing

   An XY-Wing whose pivot has three candidates (XYZ): you can remove the shared digit Z from any cell that sees the pivot and both pincers.

Techniques for Master puzzles

1. Step 13
   Skyscraper

   When a digit has only two spots in each of two rows and one end of each lines up in the same column, you can remove that digit from cells that see both of the other two ends.

2. Step 14
   2-String Kite

   When a digit has only two spots in one row and two spots in one column, and those lines meet in one box, you can remove that digit from the cell that sees both free ends.

3. Step 15
   Unique Rectangle

   Uses the fact that a proper sudoku has only one solution: four cells forming a rectangle across two boxes can't all end up as the same pair of digits, so you can remove the candidates that would make that happen.

4. Step 16
   BUG+1

   When every empty cell has exactly two candidates except one cell with three, that cell's answer is fixed — otherwise the puzzle would have two solutions.

5. Step 17
   Empty Rectangle

   When a digit's candidates in a box fit inside one row and one column (a cross), you can combine it with a line where the digit has only two spots to remove that digit from a cell.

6. Step 18
   W-Wing

   Two cells that can only be X or Y and don't see each other, linked by a line where X has only two spots, let you remove Y from any cell that sees both of them.

7. Step 19
   Naked Quad

   When four cells in a group have only four different candidates between them, you can remove those four digits from the other cells of that group.

8. Step 20
   Hidden Quad

   When four digits can only go in the same four cells of a group, you can remove all other candidates from those four cells.

9. Step 21
   Finned X-Wing

   An X-Wing with a few extra candidates (the fin) near one corner: you can still remove the digit from cells that are in the X-Wing's columns and in the fin's box.

10. Step 22
    Jellyfish

    The four-line version of X-Wing: when a digit's candidates in four rows all fall within the same four columns, you can remove that digit from the other cells of those columns.