How to use pencil marks in Sudoku

For one empty cell, begin with digits 1 through 9. Remove every digit already visible in the cell's row, then remove digits in its column, and finally remove digits in its 3×3 box. The digits left are the cell's candidates. A candidate means possible under the current grid, not proven correct.

Complete notes matter because later techniques compare candidate locations. If you write only the two digits you happen to notice, a cell may look like a pair even though a third candidate remains legal. Either maintain every candidate in the area you are analysing or clearly treat partial marks as temporary reminders rather than logical evidence.

When you place a digit, erase that candidate from every peer: the other cells in the same row, column, and box. Work locally before scanning the whole grid. One placement can remove the final alternative from a nearby cell, producing a naked single, or leave one location for that digit in a region, producing a hidden single.

If several moves have passed since your last update, stop and audit the affected regions. Stale candidates are more dangerous than missing decoration because they hide real deductions and can make an invalid elimination appear reasonable. Clever Pause's Notes mode keeps the marks attached to the grid, but the logical responsibility is still to remove each candidate only for a stated reason.

A cell with one candidate is a naked single. The note itself summarizes the proof: every other digit is blocked by the row, column, or box. Place the remaining digit, update its peers, and look for a chain. Easy and medium puzzles often release several placements from one accurate update.

A hidden single requires a different scan. Choose one digit missing from a row, column, or box and inspect the notes in that region. If only one cell contains the digit, place it there even if the cell has other candidates. The digit has one legal home in the region, which is enough evidence to resolve the cell.

When two cells in one region contain exactly the same two candidates, those digits are reserved for those cells in some order. This naked pair allows the two candidates to be removed from other cells in that row, column, or box. Both cells must share the region and neither may contain an extra candidate.

Candidate notes also expose confinement. If every candidate 6 in a 3×3 box lies in one row, the 6 must be placed somewhere along that box-row intersection. Other cells in the same row outside the box can remove 6. This locked-candidate deduction does not decide which box cell is 6; it proves only where 6 cannot appear.

You do not need to fill all 729 possible note positions at the start. Begin with crowded regions or the part of the grid where obvious singles have stopped. Expand notes consistently around the area you want to compare. The goal is a trustworthy working model, not the maximum number of tiny digits on screen.

When stuck, verify notes before searching for an advanced pattern. Pick a suspicious candidate and recheck its row, column, and box. Then scan singles, locked candidates, and pairs in that order. If a hint identifies an elimination, locate the relevant notes yourself and explain why the candidate is impossible before applying the change.