6x6 Sudoku: Rules, 2x3 Boxes and Tips for the Small Grid

A 6x6 sudoku is a smaller sudoku that uses only the digits 1 to 6. The grid has 36 squares split into six boxes of 2 rows by 3 columns, and the rule is the classic one: fill every row, every column and every box with 1 to 6 exactly once. Because the logic is the same as on the 9x9 grid with fewer squares to track, 6x6 is a good way to learn sudoku, and a quick puzzle on its own.

This guide is for beginners and for 9x9 solvers trying the small grid. It covers the rules, the shape of the grid, five tips that use the rectangular boxes, and a complete puzzle solved move by move.

The rules of 6x6 sudoku

The rules of 6x6 sudoku are the same three as in the classic game, scaled down to six digits.

1. Each of the six rows holds the digits 1 to 6, each once.
2. Each of the six columns holds the digits 1 to 6, each once.
3. Each of the six boxes, 2 rows tall and 3 columns wide, holds the digits 1 to 6, each once.

Some squares start filled. Those are the clues, and they never change. A well-made puzzle has exactly one way to fill the rest, so you never need to guess.

1	5	2	6	3	4
6	3	4	1	2	5
5	1	3	4	6	2
4	2	6	5	1	3
3	4	1	2	5	6
2	6	5	3	4	1

In this post, rows are numbered 1 to 6 from the top and columns 1 to 6 from the left. Boxes are numbered in reading order: box 1 is rows 1 and 2, columns 1 to 3; box 2 is rows 1 and 2, columns 4 to 6; and so on down to box 6 in the bottom right.

How the 2x3 boxes shape the grid

On a 6x6 sudoku the boxes are rectangles, and that gives rows and columns different jobs. On 9x9, rows and columns behave the same way, because the boxes are square.

Look at the grid in horizontal strips and vertical strips:

• Bands. The grid has three bands of two rows each. Each band holds two boxes side by side.
• Stacks. The grid has two stacks of three columns each. Each stack holds three boxes, one above the other.

So every row passes through two boxes, and every column passes through three. That small difference is behind most of the shortcuts in the tips below.

This guide uses boxes 2 rows tall and 3 columns wide. You will sometimes see the grid printed the other way, with boxes 3 rows tall and 2 columns wide. That is the same puzzle turned on its side: swap the words "row" and "column" in this guide and every tip still works.

6x6 and 9x9 sudoku compared

The 6x6 grid has less than half the squares of the classic grid, and a far smaller set of possible answers.

The grid counts and minimum clues come from the paper in which Gary McGuire, Bastian Tugemann and Gilles Civario proved the 9x9 minimum of 17 (arXiv). It credits the 6x6 minimum of 8 to Ed Russell, who checked in 2006 that no 7-clue 6x6 puzzle has a unique solution. For more on why the minimum matters, see why a good sudoku has exactly one solution.

Five tips for solving 6x6 sudoku

1. Use the band: two rows, two boxes

In 6x6 sudoku, each band of two rows holds two boxes, and every digit appears once in each row of the band and once in each box. So if a digit sits in the top row of one box, the other box in the band must have it in the bottom row. On 9x9 the same idea leaves you with two rows to choose from. On 6x6 it leaves you with one.

6	1
			2	3

2. Use the stack: three columns, three boxes

Each stack of three columns holds three boxes. When a digit already appears in two of those boxes, in two different columns, the third box must have it in the remaining column. That leaves only two squares, and often one of them is filled.

4
	4
		2

3. Finish the nearly full lines

A row, column or box with only one or two empty squares is the quickest win on a 6x6 grid. With one gap, the missing digit goes there. With two gaps, name the two missing digits, then check each gap's other row, column or box: usually one of the two digits is already there, which settles both squares at once.

4. Ask where a digit can go, not what a square can be

For each digit, look at a box and ask which of its six squares could still hold it. When only one square is left, place it. This is called a hidden single, and on 6x6 it is fast because a box has just six squares and every row and column you check rules out two or three of them. The how to play sudoku guide covers hidden and naked singles in more detail.

5. Keep notes light

A square on a 6x6 grid can have at most six candidates, and usually far fewer, so you rarely need full notes. Pencil in a pair only when exactly two squares in a row, column or box can hold a digit. If you want a system for notes, the post on sudoku notes and pencil marks explains when they save time and when they slow you down.

A full 6x6 solve, move by move

Here is a complete 6x6 sudoku with 14 clues, solved using only the tips above. A computer check confirmed it has exactly one solution. Try it yourself first, then compare.

1		2			4
		4		2
		3
	2		5	1	3
		1
2	6			4

Row 3 is the place to start. It sits in the band with row 4, which is nearly full, so box 4 already holds 1, 3 and 5.

1. Row 3 needs a 1. Box 4 already has a 1, so the 1 cannot go in columns 4 to 6. Column 1 has a 1 at the top and column 3 is filled. That leaves column 2: row 3, column 2 is 1.
2. Row 3 needs a 5. Box 4 has a 5, so again columns 4 to 6 are out, and columns 2 and 3 are filled. Row 3, column 1 is 5.
3. Row 3 still needs 2, 4 and 6 in columns 4, 5 and 6. Column 5 has a 4 (row 6) and column 6 has a 4 (row 1), so row 3, column 4 is 4.
4. That leaves 2 and 6 for columns 5 and 6. Column 5 already has a 2 (row 2), so row 3, column 5 is 6 and row 3, column 6 is 2.
5. Row 4 is missing 4 and 6, in columns 1 and 3. Column 3 has a 4 (row 2), so row 4, column 3 is 6 and row 4, column 1 is 4.

1		2			4
		4		2
5	1	3	4	6	2
4	2	6	5	1	3
		1
2	6			4

1. Row 1 is missing 3, 5 and 6, in columns 2, 4 and 5. Column 2 has a 6 (row 6) and column 5 now has a 6 (row 3), so row 1, column 4 is 6.
2. Column 1 is missing 3 and 6, in rows 2 and 5. Box 5 already has a 6 (row 6, column 2), so row 5, column 1 is 3 and row 2, column 1 is 6.
3. Column 3 has one gap. It holds 2, 4, 3, 6 and 1, so row 6, column 3 is 5. Box 5 now lacks only a 4: row 5, column 2 is 4.
4. Row 5 is missing 2, 5 and 6, in columns 4, 5 and 6. Column 5 has both 2 and 6, so row 5, column 5 is 5. Column 6 has a 2 (row 3), so row 5, column 6 is 6 and row 5, column 4 is 2.
5. Column 5 has one gap, and the missing digit is 3: row 1, column 5 is 3. Row 1 then needs only a 5, in column 2, and column 2 then needs only a 3, in row 2.
6. Row 2 is missing 1 and 5, in columns 4 and 6. Column 4 has a 5 (row 4), so row 2, column 4 is 1 and row 2, column 6 is 5.
7. Row 6 is missing 1 and 3, in columns 4 and 6. Column 6 has a 3 (row 4), so row 6, column 6 is 1 and row 6, column 4 is 3.

The finished grid is the one shown under the rules at the top of this post. Notice that no step needed notes or a guess: every move was a single, found by asking where a digit can go or what a nearly full line is missing.

Why 6x6 is a good place to start

A 6x6 sudoku teaches the habits that every sudoku needs, at a size where you can see the whole grid at once. You practise scanning for a digit, spotting nearly full lines and checking a square against its row, column and box, without nine digits and 81 squares to keep in your head.

That is why Puzzle Picnic uses the 6x6 grid for its two lower levels. Easy and Medium are both 6x6 and can be solved with singles alone; Medium simply gives fewer clues (11 to 13, against 17 to 19 on Easy). Fewer clues means each move takes a little more looking, which is good practice for the larger grid. You can try both on the Puzzle Picnic sudoku page.

A 6x6 puzzle is also short, with 36 squares and a good share of them given, so it fits a commute or a coffee break.

Moving up to 9x9 sudoku

You are ready for 9x9 when 6x6 puzzles with few clues feel routine: you find the next single without long searches, and you rarely make a mistake. The jump is real, though, and three things change.

• The boxes become square. Every row and every column now crosses three boxes, so the band trick from tip 1 leaves two rows to choose from instead of one.
• Singles stop being enough. Hard and Expert 9x9 puzzles need techniques beyond singles, starting with pointing, claiming and naked and hidden pairs and going on to X-Wing, wings and, on the hardest grids, chains. The sudoku strategies guide takes you through them in the order you will meet them.
• Notes become worth it. With nine candidates per square, light pencil marks pay off.

Frequently asked questions

How many clues does a 6x6 sudoku need?

A 6x6 sudoku needs at least 8 clues to have exactly one solution. Ed Russell checked in 2006 that no 7-clue 6x6 puzzle has a unique solution. Eight is a lower limit, not a typical count.

Are 6x6 sudoku boxes 2x3 or 3x2?

This guide uses boxes 2 rows tall and 3 columns wide. Some puzzles print them 3 tall and 2 wide. It is the same puzzle rotated a quarter turn, and the same techniques work with rows and columns swapped.

Is 6x6 sudoku easier than 9x9?

Usually, yes. It has 36 squares instead of 81 and six digits instead of nine, so there is less to scan and fewer candidates per square. A sparse 6x6 can still take some thought.

How many 6x6 sudoku grids are there?

There are 28,200,960 completed 6x6 sudoku grids with 2x3 boxes. That is large, but tiny next to the roughly 6.67 x 10^21 completed 9x9 grids.

Where to go next

If you are new to sudoku, read how to play sudoku for a first solve, then come back to 6x6 for practice. When the small grid feels easy, try a Hard 9x9 and keep the sudoku strategies guide open for the moment singles run out. More posts are on the sudoku topic page.

Sources

• arXiv: There is no 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem (McGuire, Tugemann and Civario)
• Nikoli: Sudoku rules