Sudoku is a great puzzle, but it is not about mathematics at all. To see this, note that you could substitute the letters A through I for the numbers 1 through 9, and you will have the same puzzle.
The ‘normal’ Sudoku, as most readers of the readers of this article will know, presents the solver with a 9×9 grid, divided into 9 3×3 grids. The goal is to put the numbers 1 through 9 in each row, column and smaller grid, in such a way that no row, column, or grid contains any duplicates. Some starting numbers are provided, and each puzzle has one and only one solution, which can be deduced solely through logic, with no guessing needed. They range from easy to quite difficult, and can involve some quite complex skills – there are even books on how to solve Sudoku puzzles.
As such, they are great for the development of certain logical skills, and they can teach you to be careful and accurate in your solving (get one thing wrong, and everything that follows will be messed up) but they aren’t about math. As I said above, you can just substitute letters for the numbers, and it’s still the same puzzle.
Still, logic is the basis of a lot of math, and improving logical skills will probably improve mathematical reasoning, in an indirect way.
For a similar puzzle that does involve math much more directly, try KenKen. In a KenKen puzzle, you are presented with a square grid (it can be 3×3 or larger), ruled off into smaller boxes. Each box has a single number in it, along with an arithmetic symbol (+, -, x, or /). The goal is to fill in the numbers so that each box adds, subtracts, multiplies or divides to the number given. This is a lot easier to see with an example, e.g. http://www.kenken.com/#.
At the easiest levels, this will teach basic arithmetic facts; but at higher levels, you will learn, intuitively, about prime vs. composite numbers, factors, and so on. It’s a lot of fun!
Yet another type of puzzle is sometimes known as “cross sums” or Kakuro, you are presented with a crossword like grid, only the clues are numbers, rather than the usual crossword clues, and the grid is to be filled with numbers, rather than letters. Here, however, there is only addition. This will certainly help with some basic math facts, and may also provide some insight into the natural numbers, but I think KenKen will do much more for mathematical reasoning.
