4×4 Sudoku

That makes it the quickest way to see what “only one digit can go here” means before moving to a larger grid.

How does the 4×4 board work?

The grid is four rows by four columns. Each 2×2 box holds four cells, and the digits 1 to 4 each appear once in every row, column and box. The rules are exactly those of classic Sudoku, only shrunk. The rules page states them in full, and the controls page lists every key and button.

Because the board is so small, every cell sees very few others. A cell shares a row with three cells, a column with three, and a box with three, but one of its box neighbors is already in its row and one in its column, so it has seven peers in total. A classic cell has twenty. With seven peers, a digit placed in one cell rules itself out of nearly half the board.

What do the stored puzzles look like?

The site holds 30 puzzles for this board, all at the Easy level. Each starts with four or five givens, with an average of 4.3. Every puzzle was checked to have exactly one solution, and every one is solved by the technique solver using naked singles only. In the measured sample, hidden singles and every higher technique are never needed, which is why only the Easy level exists. The site does not offer a Medium or Hard 4×4 because no stored puzzle needs more than the first technique.

A puzzle with only four or five givens and a single solution is tightly balanced. The generator keeps removing givens until removing any more would either give the puzzle a second solution or make it need more than naked singles. This is the same idea that governs the 9×9 puzzles, which the guide on how puzzles are generated and verified unique explains.

A first solve, cell by cell

The method is the one used for Easy puzzles on every board. Pick a cell, list the digits its row, column and box already contain, and see what is missing. With only four digits in play, the list is short. If a cell sees 1, 3 and 4 among its peers, it can only be 2. This is a naked single, and it is the only technique this board asks for.

A good habit is to start with the box, row or column that has the most givens. If a box holds three digits, the fourth cell is forced immediately. Write that digit in, and then look at the cells that share a row or column with it, since they now have one fewer option. In most of these puzzles a chain of such placements runs to the end of the grid.

What is the 4×4 board good for?

• Learning the rule. A whole solve takes a minute or two, so you can see the logic from start to finish without tracking eighty-one cells.
• Practicing the scan. The cell-by-cell habit is the same one you will use on 6×6 and on the classic board.
• Checking your reading of the box rule. The 2×2 box is the easiest box to get wrong when you are new, and a small board makes a mistake quick to find.
• A warm-up. It is a short exercise before a longer session.

What is missing, and why?

This board has one level and no Evil puzzles, and it has no hidden single practice. For hidden singles, which look at where a digit can go rather than what a cell can hold, you need a larger grid. The hidden singles lesson shows the idea on a classic board, and the 6×6 board is the next step up, where a hidden single is needed in some puzzles.

Hints, notes and undo all work as on the other boards. On such a small grid you will rarely need pencil marks, though you can try them with the Notes button. The guided first puzzle narrates the same reasoning on a full 9×9 board.

Where should you go next?

Once the 4×4 board feels automatic, move to the 6×6 board, which adds rectangular boxes and a second level. After that, try Easy on the classic board from the home page. If you would like a different extra rule on a 9×9 grid, the diagonal board is a gentle start. The games hub lists every board, including the 16×16 board, which applies the same rules at the other extreme, and the complete solving guide shows where the technique ladder leads after singles.