Solving a 4×4 sudoku:
one rule is enough

The grid is filled with the digits 1 to 4. Every row, every column and each of the four 2×2 squares contains each digit exactly once.

The four squares of a 4×4 sudoku.

Along with the classic 9×9, it is the only format on Sudoku-Land whose blocks are true squares. As a result, rows and columns play exactly the same part. Each one crosses 2 squares, and ruling out a row or a column always removes 2 cells out of 4 from a square. There is no preferred scanning order, unlike the 6×6 and 8×8 grids, whose rectangular blocks favour rows.

A 4×4 grid is small enough for a program to go through all of them. We did, and here is what comes out:

• there are 288 different completed 4×4 grids;
• a puzzle needs at least 4 given digits to have a single solution — true for 25,728 starting grids, never with 3;
• of the 13,579,680 starting grids with a unique solution, none requires guessing, or any advanced technique.

For an adult helping out, this is valuable. It means that as long as no mistake has been made, there is always a safe cell somewhere, and you can honestly tell the child: “there has to be one, let's find it.” The next three sections are three ways to find it.

This is the most natural deduction. A row with three digits already placed has only one answer for its fourth cell. The same goes for a column or a square.

But it also works when no area is nearly full. Every cell “sees” 7 other cells: 3 in its row, 3 in its column, and 1 more in its square. If those 7 cells already hold three different digits, the fourth is the only one left:

A 2 in the square, a 1 in the row, a 4 in the column: it is a 3.

That is why Kids Sudoku 4×4 has no notes mode: with only four digits, everything fits in your head.

The other way to search starts from a digit rather than a cell: “where does the 3 go in this square?” A square has only two rows and two columns, and this is where the 4×4 becomes elegant.

• a 3 in the square next to it rules out a row: 2 cells out of 4 gone;
• a 3 in the square above or below rules out a column: 2 more cells, one of them already gone.

Three cells out of four ruled out: only one is left.

The ruled-out row and column cross: the 3 of the top-left square has only one cell left.

The cross has an even quicker consequence. The top-left and bottom-right squares are diagonal: they share no row and no column. But for the top-right square, one of them is “next to it” and the other is “below” — and the same holds for the bottom-left square.

So as soon as a digit is placed in two diagonal squares, the cross rule places its other two copies at once:

Two diagonal 2s are enough to place every 2 in the grid.

This deduction only exists in 4×4. In a 9×9, a digit placed in two boxes still leaves plenty of choice for its seven other copies. Here, two well-placed copies give you all four.

For the right age, which grid to pick and what to do when your child gets stuck, see our guide How to Teach a Child Sudoku. Here we only cover the method: how to pass on these three deductions without a lecture.

1. Start with the missing digit, on an almost full row. “There's a 1, a 2 and a 4. What's missing?” It is the only deduction that needs just one area at a time.
2. Show the cross with your fingers. Put one finger on the ruled-out row and another on the ruled-out column: the cell left free between them is the answer. The gesture beats any explanation.
3. Ask why. “Why not here? — Because there's already a 3 in this row.” A child who can justify a cell has understood the game, even if still slow.
4. Save the diagonal for later. It is a reward, not a starting point. When a child finds it on their own, they have turned a corner.

And when nothing comes, remind them of the rule above: there is always a safe cell. The game's 🆘 Help button does exactly that: it animates the grid to show where to look, without giving the digit away.

1. Guessing. It is never needed in 4×4, and a random mistake costs you three cells later. If a child hesitates between two digits, that is the sign another cell is easier.
2. Forgetting the squares. Rows and columns are obvious; squares much less so. A digit that respects its row and column can still be doubled in its square.
3. Filling a pair at random. Two empty cells in a row: you know both digits, not their order. The column or the square of one of the two cells usually settles it; if not, move to another cell and come back later.

Kids Sudoku 4×4 offers free easy kids sudoku puzzles at three levels — Easy, Medium and Hard — with colour-coded digits, the 🆘 Help button and a stats panel to track progress. The grids can also be printed to play on paper.

Once the 4×4 no longer puts up a fight, Junior Sudoku 6×6 is the next step: its blocks become 2×3 rectangles, and some reflexes change — see our article Solving a 6×6 Sudoku.