6×6 Sudoku

It offers two levels, Easy and Medium, with 150 stored puzzles each, and the step between them is the first time you need more than singles.

What is different about the 6×6 board?

Two things set it apart from both the small 4×4 board and the classic board. The grid is six cells wide, so a row has six cells and a digit set of 1 to 6. And the boxes are rectangles, two rows by three columns, instead of squares. Three boxes sit side by side in the top half of the grid and three in the bottom half, so the grid is split into two bands of three boxes. The rules page gives the full statement, and the controls page covers input.

The rectangular box has a consequence for solving. A box shares three cells with each row it touches but only two with each column. Every cell has twelve peers, five in its row, five in its column and two more in its box. The board also has no mirror symmetry along the diagonal, because a 2×3 box turned on its side is a 3×2 box, which the grid does not contain.

How many givens do the puzzles have?

The stored puzzles hold between 8 and 12 givens, with an average of 10.2 on Easy and 10.0 on Medium. As on the classic board, the clue count barely changes between levels, so the number of givens tells you nothing about difficulty. What changes is the technique required. Each puzzle is verified to have exactly one solution.

What does each level need?

In the stored sample of 150 puzzles per level:

• Easy: every puzzle uses naked singles, and 32% also use hidden singles. About two in three are solved by naked singles alone.
• Medium: hidden singles appear in 96% of puzzles, and pointing pairs in 97%. Box/line reduction appears in 6%, naked pairs in 3% and hidden pairs in 2%.

The striking number is the pointing pair: nearly every Medium puzzle uses one. One plausible reason is that a box covers three cells of a row, so a digit’s remaining places in a box often line up along a single row, though the data does not prove that. When they do line up the digit can be removed from the rest of the row. The pointing pairs lesson explains the deduction, and you will be using it here much sooner than on the 4×4.

A short strategy for the 6×6 board

1. Start with the digits that appear most often. A digit that is already in four or five cells has only one or two places left.
2. Check rows by box. Because a box is three cells wide, looking at which two boxes of a band already hold a digit shows where the third must put it.
3. Write notes when the singles stop. The pointing pair needs candidates to be visible, and the pencil marks guide shows how to keep them tidy.
4. Look along rows for pointing pairs. They are the likely next move on Medium, and you can find them quickly by asking which row a box’s digit is confined to.

Why does the board stop at Medium?

The generator only keeps a puzzle in a level if the technique solver needs that level’s techniques. For 6×6 it produced puzzles at Easy and Medium. The board has no Hard, Expert or Evil puzzles, and the site does not label one that has not been earned. The grading logic is described in how Sudoku difficulty is graded.

How does it help with the classic board?

The 6×6 board is a bridge. It contains the same two ideas as classic Easy and Medium, singles and pointing pairs, but on a grid you can hold in your head. If you can finish the Medium level reliably, the step to the classic board’s Medium level is mostly a matter of scale. If you are coming from the 4×4 board, this is the point where you first need to think about where a digit can go and not only what a cell can hold. If you would like a new rule on a 9×9 grid, the diagonal board is a gentle next step. When you want a bigger challenge in the other direction, the 16×16 board scales the same rules up. The games hub lists all the boards, and the home page has the classic game.