A little practice. A little progress.

Sudoku techniques: candidates before guesses

Learn two reliable ways to place a number, then see how locked candidates and pairs help when singles run out.

Start with the three constraints

In a 9×9 Sudoku, each row, column and 3×3 box contains 1 through 9 once. A 4×4 uses 1 through 4 and 2×2 boxes; a 6×6 uses 1 through 6 and boxes two rows high by three columns wide. No arithmetic is needed for classic Sudoku.

A candidate is a number not already used in the cell’s row, column or box. Notes record possibilities; they are not commitments. Recheck them after every placement, because a number elsewhere can rule one out.

1. Single candidate: one number fits this cell

Look at the highlighted top-left cell in this original 4×4 example. Its row already has 1. Its column has 2. Its box has 3. The only remaining candidate is 4.

So row 1, column 1 must be 4. You have used all three constraints together, rather than choosing a number that merely looks plausible. This is also called a naked single.

2. Hidden single: one cell fits this number

Now reverse the question. Instead of asking which numbers fit a cell, choose a number and ask where it can go within one row, column or box.

In row 1, the empty columns are 1, 2, 4, 5, 7 and 9. Column 1 already contains 3 at row 7; column 4 has 3 at row 2; column 5 is blocked by the 3 in its top-middle box; column 7 is blocked by the 3 in its top-right box; and column 9 already contains that 3 at row 3. Only column 2 remains.

Place 3 at row 1, column 2. That cell can have several candidates before the deduction; 3 is forced because it has no other home in the row. This is a hidden single, or an only-place deduction.

3. Locked candidates: use a box and a line together

If every possible location for 7 inside a box lies in the same row, that box’s 7 must occupy that row. Remove 7 from candidates in the rest of the row outside the box. The same argument works for columns.

The reverse also works: if all places for 7 in a row fall inside one box, remove 7 from other cells in that box outside the row. A locked candidate eliminates possibilities; it does not always immediately place a number.

4. Naked pairs: reserve two digits

Suppose exactly two cells in one row each have the candidate set {2, 5}. One must be 2 and the other 5, although you may not know which. Remove 2 and 5 from every other candidate set in that row. The same rule applies within one column or box.

Both cells must contain only those two candidates. A cell marked {2, 5, 8} is not part of a naked pair. After eliminations, look again for singles.

A calm solving loop

1. Scan nearly complete rows, columns and boxes.
2. List candidates for a few promising empty cells.
3. Check for single candidates and only-place deductions.
4. If stuck, inspect boxes and lines for locked candidates, then pairs.
5. After each placement, update notes and repeat the scan.

If a contradiction appears, revisit recent entries and use Undo. A conflict-free entry is not necessarily correct: it can still prevent a solution later. Matte’s explained hints highlight a cell, explain the deduction and wait for you to choose whether to apply it. Technique ratings describe the methods our tutor can verify; an ungraded puzzle is not automatically an expert puzzle.

Practice one technique at a time

The illustrated positions come from our original interactive lesson set. Try the four interactive lessons for feedback, or use printable puzzles with separate answers for pencil-and-paper practice.