The Standard 9x9 Sudoku puzzle has 9 rows, 9 columns and 9 square blocks of size 3x3.
Other sizes of Standard Sudoku are 4x4 (very easy), 16x16 and 25x25 (not so easy).
The Jigsaw and Aztec variations are the same as Standard 9x9 Sudoku except that some blocks are not square.
The XSudoku variation is exactly the same as Standard Sudoku with an additional requirement: the two main diagonals must also each contain the symbols 1 to 9 once and once only. KSudoku highlights the diagonals to make this easier to see.
The Nonomino 9x9, Pentomino 5x5 and Tetromino 4x4 variations are the same as a Standard Sudoku except that some blocks are not square.
The 6x6 variation is the same as a Standard Sudoku except that the blocks are six 3x2 rectangles.
The Samurai Sudoku consists of five Standard Sudoku puzzles of 9x9 squares each, overlapping at the corners by four 3x3 blocks. Each of the five puzzles has 9 rows, 9 columns and 9 blocks to solve and the symbols in the overlapping squares must fit into the solutions of two Standard 9x9 Sudokus.
The Tiny Samurai Sudoku contains five 4x4 Sudoku puzzles, overlapping at the corners by four squares. Each of the five puzzles has 4 rows, 4 columns and 4 blocks to solve.
The Windmill variation consists of five Standard 9x9 Sudoku puzzles, overlapping at the corners by two 3x3 blocks. It is like a Samurai Sudoku, but the central 9x9 Sudoku is harder to see. Eight of its 3x3 blocks are shared with the sails of the windmill and only the central 3x3 block is not.
The Sohei variation is another Samurai type and has four 9x9 Sudoku puzzles, overlapping at two corners by a 3x3 block. The central 3x3 block of the puzzle is empty.
The Roxdoku variants are based on cubes in three dimensions, but are easier than they sound. There are no rows or columns. A 3x3x3 Roxdoku puzzle has 27 small cubes arranged into a larger 3x3x3 cube. This contains nine slices, each containing 3x3 small cubes, and these are the square blocks that must be filled with the numbers 1 to 9. A 4x4x4 Roxdoku has twelve 4x4 slices and a 5x5x5 Roxdoku has fifteen 5x5 slices.
The Roxdoku Twin variant has two 3x3x3 Roxdoku puzzles sharing a corner. The corner piece must be part of the solution of both 3x3x3 cubes.
The Double Roxdoku variant contains two 3x3x3 Roxdoku puzzles sharing three pieces along an edge. The edge pieces must be part of the solution of both 3x3x3 cubes.
The Samurai Roxdoku variant has nine 3x3x3 Roxdoku puzzles. One is at the center and the other eight 3x3x3 cubes overlap it, one at each of the central cube's corners. Those corner pieces must each be part of the solution of two 3x3x3 cubes.
Killer puzzles have two variants: Tiny Killer (4x4) and Killer Sudoku (9x9). They both have rows, columns and square blocks, exactly as in Standard Sudoku puzzles and following exactly the same rules. They also have irregularly shaped areas called cages, where each cage's digits must add up to the number in small type in the corner of the cage and no digit can be repeated within the cage. Typically the puzzle starts with only a few squares containing symbols. You need to use arithmetic and the usual Sudoku rules together to work out the solution. The screen graphics make it difficult to visualize the square blocks that are present, but they are easier to see if you print the puzzle, using the → menu item.
Mathdoku variants, also known as Kenken™, have no blocks, only row and column restrictions, and have cages where the digits must add, subtract, divide or multiply according to the values and arithmetical symbols in small type in their corners. A digit in a Mathdoku cage can be repeated, but not in the same column or row. For example, an L-shape of three squares with a requirement 5+ can have solutions 1 3 1 or 2 1 2, provided the ones or twos are not in the same row or column as each other. Note that subtraction and division cages always have two squares and the two digits of the solution can appear in either order. For example, a 2-cage could have solutions 1 3 or 3 1 or 2 4 or 4 2, etc.
Because there are no blocks in a Mathdoku puzzle, it can have any size from 3x3 up to 9x9, with the default being 6x6. See the Game Configuration section for details. To get you started, there is a variant called Mathdoku 101 of size 4x4.