Dokusu logo

Dokusu main screen

Dokusu Main Screen

Winning square

Winning square

What is Dokusu?

Dokusu is part Sudoku, part slider puzzle with a math lesson on the side. It borrows from both the enormously popular Sudoku and from classic slider games like 15-Square, but adds an interesting topological twist. Play it for fun or use it as an educational aid to explore pemutation group theory concepts.

Dokusu is simple enough to be played by elementary school children, but challenging for all ages. The mathematical concepts are targeted at upper high school and undergraduate college level students.


Move the tiles horizontally and vertically to form a 4x4 Sudoku square. A Sudoku square has no repeating numbers in any of the four columns, rows or 2x2 corner blocks. A picture of a winning square is shown below on the right.

Moving a tile horizontally causes all the tiles in that row to shift circularly. As tiles move off the board on one side, they enter the board on the other side. Similarly, moving tiles vertically causes columns to shift circularly. Diagonal moves are not allowed, although it is possible to move a single tile in a diagonal direction by moving it horizontally and vertically.


Dokusu is available now for the Apple iPhone and iPod touch on the App Store.
Dokusu on the App Store

Dokusu Mathematics

There are 288 possible solutions for a 4x4 square. This is relatively simple to prove. A more interesting, but more difficult, Dokusu math question is:

How many solutions can be achieved (reached) for a given initial arrangement? (Hopefully at least one!)

Slider on a torus

Slider on a torus

Dokusu is topologically a slider on a torus. No, that is not a fast food item. A very nice rendering of a slider on a torus is on the left. An even fancier rendering can be found here: Dokusu Supreme.

There are probably not many other renderings of a slider on a torus.

A more detailed analysis of Dokusu mathematics is presented in the application.