earnmath.com · interactive lab

The Sudoku Math Lab

Sudoku looks like a number puzzle, but underneath it is pure mathematics: constraints, symmetry, and counting on a scale that is hard to imagine. Try both labs below.

A 6×6 warm up grid

Every row, every column, and every 2×3 box must contain the numbers 1 through 6 exactly once. Tap an empty cell, then tap a number. Watch what happens when a number repeats where it should not.

Select a cell to begin.

One grid, endless twins

Start with one valid, completed grid. Each button below applies a transformation that mathematicians call a "validity preserving symmetry." No matter how many times you press, the result is still a perfectly valid Sudoku.

Transformations applied: 0
This is the grid we are starting from. It is a small 4×4 version of Sudoku, used here just to make the symmetry tricks easy to see. A full 4×4 grid has only 288 valid completed solutions in total, compared to the mind bending 6,670,903,752,021,072,936,960 for a real 9×9 grid.