Three Sudoku strategies for your next grid

One square, one possibility

A naked single is a square with only one possible digit. If a square's row, column, and box already exclude 1, 2, 3, 4, 5, 6, 8, and 9, the square must be 7. This is a certainty, even when it takes a little scanning to see it.

Write the remaining possibilities in Notes when the square is less obvious. Check them again after placing nearby digits.

One digit, one home

A hidden single works in the opposite direction. Instead of asking what can fit in one square, ask where a particular digit can fit in a row, column, or box.

Imagine a box is missing a 6. Columns containing a 6 and rows containing a 6 rule out most empty squares in that box. If only one square remains, it must contain the 6, even if that square has other pencilled possibilities.

• Choose a digit with several appearances in the grid.
• Look across one band of three boxes.
• Use the occupied rows and columns to eliminate positions.
• Place the digit only when one position remains.

When a box points to a line

Suppose the only places for 4 in a box lie in the same row. A 4 must occupy one of those places, so the rest of that row outside the box cannot contain 4. You may not know the final square yet, but you have learned something useful. This is a locked candidate.

Remove 4 from notes in the rest of that row. The same reasoning works with a column.

Keep the loop small

After every certain placement, scan the affected row, column, and box again. New singles often appear immediately. Before learning many techniques, become comfortable with this loop: observe, place, update notes, scan again.

If you stall, widen your view rather than choosing a digit at random. There is no penalty for taking your time. Try a Medium puzzle and look for one hidden single you can explain.