Mini Sudoku (6x6)
A six-by-six grid with the digits 1 to 6, divided into boxes that are three cells wide and two cells tall. Every digit appears once in each row, once in each column and once in each of the six rectangular boxes. The pad under the board carries six digits rather than nine, and most people finish one of these in a few minutes without writing anything down.
The box is a rectangle, and that is the whole difference
Nine and four are square numbers, so their grids divide into square boxes. Six is not, so the shape usually written 6×6 has to use a rectangular box instead: three across and two down. That asymmetry is the thing to keep in mind while solving. A row passes through only two boxes rather than three, and it crosses each of them for three cells at a time, while a column passes through three boxes and crosses each for two cells. Scanning across the grid and scanning down it are no longer the same job, and the vertical scan is the one people forget.
Twelve peers instead of twenty
On a nine-by-nine grid each cell shares a unit with twenty others. Here the arithmetic is five in the row, five in the column, and then the box: it holds six cells, five of them other than yours, but three of those five are already counted because two share your row and one shares your column. That leaves two genuinely new cells, for twelve peers in total. A digit you write here constrains a little over half as much of the board as the same digit on a full grid, which is the real reason the puzzle is quicker – not that the grid is smaller, but that each move does less work.
There are exactly 28,200,960 finished six-by-six grids
Small enough to count by brute force, and the count is worth seeing next to the full-size figure, which runs to twenty-two digits. Hold the top row at 1 2 3 4 5 6 and 39,168 legal ways to fill the remaining five rows survive. Any other top row is one of those solutions with the symbols renamed, and there are 720 ways to rename six symbols, so 39,168 multiplied by 720 gives the total. Twenty-eight million sounds like plenty until you notice it would fit in a few gigabytes – which is exactly why nobody stores them and every board here is built when the page loads.
Hidden singles are easier to see on this shape
The classic scan – pick a digit, find the one box it has to go in – is less work here because each box has only six cells and two rows. If a 4 already sits in one of the two rows a box occupies, it is confined to three cells immediately, and one more crossing column usually settles it. On a nine-by-nine the same argument leaves three cells and needs two further eliminations. That is why a mini sudoku suits a solver who wants the deduction without the search.
Between the four-by-four and the full grid
This size sits usefully between a four-by-four, where the whole logical world fits in one glance, and a nine-by-nine, where you eventually have to write candidates down. It is the largest grid most people can hold entirely in their head, which makes it the right one for a bus journey or for practising a technique you have just read about rather than for a long sitting.