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MAKE THE NEXT MOVE MAKE SENSE

Sudoku strategies, one step at a time.

A useful Sudoku move has a reason you can point to on the board. Begin with simple deductions, update your candidates, then look for patterns that remove possibilities. The examples below describe local patterns; each deduction assumes that your existing entries and candidate lists are correct.

1. Naked singles: one candidate in a square.

For an empty square, cross off every digit already present in its row, column or box. If just one digit remains, you have a naked single. Suppose the combined clues around a square rule out 1, 2, 3, 4, 6, 7, 8 and 9. Only 5 remains, so that square must contain 5.

Look again after each placement. A new 5 may remove a candidate from another square and turn it into a single. A short chain of simple moves can open a board that first looked crowded with possibilities.

2. Hidden singles: one place for a digit.

Change the question from “What fits in this square?” to “Where can this digit go in this group?” Choose a missing digit and inspect every empty square in a row, column or box. If only one square can accept it, the digit belongs there even when that square has other candidates.

For example, a row is missing 2, 5 and 8. Its three empty squares have candidates {2, 5}, {2, 5} and {2, 5, 8}. Only the third square can hold 8. That is a hidden single; you do not need to decide between 2 and 5 yet.

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

Suppose every possible position for 6 inside the top-left box lies in the top row. That box must contain a 6, and wherever it lands, it will occupy the top row. You can therefore remove 6 from candidate lists in that row outside the box.

The reasoning also works in the other direction. If all possible positions for a digit in a row lie inside one box, remove that digit from the other squares of that box. Columns work the same way. An elimination may expose a single elsewhere; it does not always produce an immediate placement.

4. Naked pairs: two squares reserve two digits.

If two squares in one row both have exactly the candidates {3, 7}, those squares must contain 3 and 7 in some order. Remove 3 and 7 from every other square in that row. The same pattern works within a column or a box.

Both squares must have only those two candidates. A square marked {3, 7, 9} does not form this pair. Also keep the deduction inside the shared row, column or box: two matching notes in unrelated squares tell you nothing by themselves.

How these techniques match our levels.

Sudoku Dawn rates classic puzzles with its own logical solver. Easy puzzles can be completed with naked singles. Medium adds hidden singles. Hard adds locked candidates and naked pairs. Expert goes beyond this supported set; the label does not mean that guessing is required. Difficulty labels can differ between Sudoku websites.

The teaching hints currently explain naked and hidden singles only, including on harder puzzles. If you get stuck, recheck your notes and recent entries before trying a more advanced pattern. A missing candidate can make a sound deduction appear impossible, while an extra candidate can hide the next useful move.