How to Solve Killer Sudoku: Learn the Techniques Step by Step

Killer Sudoku Rules: How to Play Killer Sudoku · Killer Sudoku Cage Combinations Chart (2–9 Cells, All 502)

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.

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

   When a cell has only one candidate left after considering its row, column, box, and cage, that candidate is its answer.

3. Step 3
   Cage Combinations

   Narrows down which numbers can go in a cage from its total and number of cells; a number that appears in none of the possible combinations can't go in the cage.

Techniques for Easy puzzles

1. Step 4
   Rule of 45 (Innies & Outies)

   Uses the fact that every row, column, and box adds up to 45: subtract the cages that fit inside to find the total of the cells that stick in or out.

Techniques for Medium puzzles

1. Step 5
   Cage Pointing

   When a number must go in a cage and all its possible cells there lie in one row, column, or box, you can remove that number from the rest of that row, column, or box outside the cage.

2. Step 6
   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.

3. Step 7
   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 8
   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 9
   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 10
   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 11
   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 12
   Rule of 45 (Several Rows or Columns)

   Applies the Rule of 45 to two or three neighboring rows or columns (or two boxes) at once — 90 for two lines, 135 for three — subtracting the cages that fit inside.

2. Step 13
   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).

3. Step 14
   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.

4. Step 15
   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.

5. Step 16
   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 17
   Innie-Outie Difference

   A step beyond the Rule of 45: it finds the difference between a cell missing inside a row, column, or box and a cell sticking out, which narrows down both numbers.

2. Step 18
   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.

3. Step 19
   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.

4. Step 20
   Unique Rectangle

   Uses the fact that a proper puzzle 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.

5. Step 21
   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 22
   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 23
   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 24
   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 25
   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 26
    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.