Solve a Mini Sudoku step by step

Mini Sudoku uses the same logic as the full-size puzzle, on a board small enough to take in at once. Here’s a complete solve with a reason for every number, using three questions you can carry to any board.

The rules: every row, every column and every box holds the numbers 1 to 6 exactly once. The boxes are three cells wide and two tall; in the diagrams they’re the alternating shaded and unshaded blocks. Starting numbers are dark, numbers we’ve added are in colour, and an outline marks the cells added in each step. Rows count down from the top and columns across from the left.

1. Rule out five numbers

Take row 3, column 2. Its row already has a 3 and a 6. Its column has 3, 5, 4 and 1. Its box, the middle-left one, has 3, 4 and 5. Together they rule out 1, 3, 4, 5 and 6, so the cell must be 2.

Its neighbour, row 3, column 3, works the same way. The row now has 2, 3 and 6, the column has a 5, and the box has 2, 3, 4 and 5. The only number left is 1.

2. Fill the last gaps

Those two numbers leave the middle-left box and column 2 with one empty cell each. The box now has 1, 2, 3, 4 and 5, so its last cell, row 4, column 1, is 6. That leaves row 4 missing only a 2, in column 4. And column 2 now has 1, 2, 3, 4 and 5, so its last cell, at the bottom, is 6.

3. Ask where a number can go

Row 2 has five empty cells, so asking what goes in each one gets you nowhere fast. Turn the question round: where in row 2 can the 1 go? Not column 1 or column 3, because the top-left box already has a 1. Not column 5, which has a 1 in row 4, and not column 6, which has a 1 at the bottom. That leaves column 4, so row 2, column 4 is 1.

Now do the same for 3. Column 1 has a 3 in row 3, the top-left box has a 3, and column 6 has a 3 in row 4. Column 4 is taken by the new 1, so the 3 goes in column 5.

Sudoku players call this a hidden single. The cell itself could still hold several numbers, but the number has nowhere else to go.

4. Another hidden single

Try the same question on row 5: where can the 6 go? Column 1 has the 6 from step 2, the bottom-left box has the 6 at the foot of column 2, and column 5 has a 6 in row 3. Only column 6 is left, so row 5, column 6 is 6.

That opens up column 6. Row 2, column 6 can’t be 1, 3 or 5, which are in its row, or 2 or 6, which are in its column, so it’s 4. Column 6 is then missing only 5, in row 3.

5. Tidy up the top

The top-right box now has 1, 2, 3, 4 and 5, so its last cell, row 1, column 4, is 6. Row 1 is then missing only 4, in column 3. Row 2 still needs 2 and 6 in columns 1 and 3. Column 1 already has a 6, so the 2 goes in column 1 and the 6 in column 3. Finally, row 3 is missing only 4.

6. Finish with the columns

Column 4 has one gap left, in row 6, and its missing number is 5. For the rest, compare each column’s missing numbers with what row 5 needs, which is 2, 4 and 5. Column 3 is missing 2 and 3, and only the 2 fits row 5, so row 5 takes the 2 and row 6 the 3. Column 5 is missing 2 and 4. Row 5 has its 2 now, so it takes the 4 and row 6 gets the 2. That leaves 5 for row 5, column 1, and 4 for the bottom-left corner.

Three questions for your next board

Three questions did all the work here. Is there a row, column or box with one gap? Is there a cell where its row, column and box rule out five numbers? And in a busy row, column or box, where can each missing number go? Cycle through them, and after every placement look again at the row, column and box you just changed.

Harder boards sometimes need more than this, but these three questions get you a long way. This board was made for the lesson and checked for a single solution; it isn’t from the Daily set or the Weekly collection. When you’re ready, try Mini Sudoku in the Library, or read the Mini Sudoku guide for the rules and controls.