Sudoku Variations

Classic Sudoku

Sudoku is the logic puzzle popular around the world. The rules are simple, but the puzzles can be extremely challenging, making for a stimulating diversion. The objective is to fill a 9x9 grid with the digits 1-9 so that
  • Each row contains each of the digits 1-9 exactly once,
  • Each column contains each of the digits 1-9 exactly once, and
  • Each 3x3 subgrid contains each of the digits 1-9 exactly once.
In a Sudoku puzzle, several of the squares of the grid are prefilled with digits. The player must fill in the rest of the squares to solve the game.

One additional (and essential) property of every Sudoku puzzle is that there is a unique solution to the puzzle.

Sudoku-X

In a Sudoku-X puzzle, each of the main diagonals (from upper left to lower right and from lower left to upper right) must contain the digits 1-9 exactly once. These additional constraints can often be used to help find the solution to the puzzle.

The diagonal squares are shaded to indicate that you are playing Sudoku-X.

The "X" factor can be added to any of the puzzles described below, leading to several additional puzzle types, all of which will appear on my site.

Greater-than Sudoku

In a Greater-than Sudoku puzzle, the objective is the same: Fill each square with a digit so that each row, column, and subgrid contains exactly one of each digit 1-9. However, the clues given follow a completely different pattern. None of the squares is prefilled with a digit. Instead, clues are given that represent relationships (less than or greater than) between adjacent squares. Logically following these clues will enable you to eliminate values from squares, eventually leading to a unique solution to the puzzle.

Killer Sudoku

Killer Sudoku introduces a little bit of arithmetic to a Sudoku puzzle, using the concept of a cage. A cage is a group of adjacent squares, enclosed within a dashed border. The following rules apply to cages:
  • A cage cannot contain any duplicate entries.
  • In the upper left hand corner of a cage is a numeric value. The sum of the digits in the cage must be equal to this value.
Because of the additional information given by the cage sums, the puzzle contains no prefilled squares. But the cage sums give a significant amount of information about the contents of the squares. As a simple example, in a 2-square cage with a sum of 5, there are only two ways to fill it in: with a 1 and 4, or with a 2 and 3. A unique solution can be found by logical deduction from the cage structure and sums.

Greater-than Killer Sudoku

As the name indicates, Greater-than Killer Sudoku combines some of the features of Killer Sudoku and Greater-than Sudoku puzzles:
  • The puzzle contains cages, subject to the same rules that apply in Killer Sudoku.
  • Less-than and greater-than symbols appear throughout the puzzle. However, instead of applying to the contents of individual squares, these constraints apply to the sums of values in the corresponding cages. "=" signs are also used to indicate that two adjacent cages contain equal sums.
  • Because of the additional clues given by the less-than, greater-than, and equals constraints, some of the cage sums are missing. The player must use the constraints to deduce the cage sums in order to fill in the puzzle squares.