Solving techniques · An interactive read
Sudoku Scanning: Follow One Digit to a Forced Cell
Use rows, columns and boxes to narrow a digit's locations, and learn when a scan gives a placement or only a restriction.
The idea to take away
A useful scan asks one precise question. Eliminate locations for a digit until one remains—or record the restriction and move on.
Give your eyes a question
Scanning means inspecting a defined part of the board for a defined reason. “Where can 7 go in the top-left box?” is a question you can finish. Looking for any useful shape anywhere is much harder to track.
Conceptis describes scanning in one direction and then combining perpendicular restrictions. [1] We will use that idea with an original fragment containing only a few placed 7s. Other digits are omitted so the exclusion pattern is visible. The fragment teaches a deduction; it is not a full Sudoku to solve or a claim about the difficulty of a particular puzzle.
Read coordinates as row then column. The upper-left cell is r1c1; the lower-right is r9c9.
Cross out locations, not whole digits
In the first diagram, row 1 already contains 7 at c4, and row 2 contains 7 at c7. Therefore no cell in either of those rows can hold another 7. Inside the top-left box, only its bottom row remains available.
Now use the perpendicular evidence. Column 1 already has 7 at r4; column 2 has 7 at r7. Those columns exclude r3c1 and r3c2. The sole remaining position in the box is r3c3. Because the box needs a 7, place it there.
Notice which information mattered: the four placed 7s and the requirement that box 1 contain 7. You did not need to calculate candidates for every other digit. This digit-and-box search is often called crosshatching in explanations of hidden singles. [2]
Know when the scan has not finished
Remove the two column clues from that example. The second diagram still blocks rows 1 and 2, but r3c1, r3c2 and r3c3 all survive. The scan has proved that the box's 7 lies in row 3. It has not proved which of those cells contains it.
Keep that distinction explicit. You may be able to use the restriction for a pointing elimination elsewhere in row 3, but you cannot fill one of the three cells arbitrarily. A partial result can be valuable without being a placement.
Stuart's starting guide likewise checks restrictions from intersecting houses to identify the final location. [3] When a scan leaves several survivors, seek another constraint or switch questions.
Use a new answer as the next starting point
Suppose you have just placed the proved 7 at r3c3. Other empty cells in row 3, column 3 and box 1 can no longer contain 7. Those are natural places to inspect next because their possibilities have changed.
After updating them, ask two questions. Did a cell lose all but one candidate? Did a missing digit lose all but one location in one of those houses? The first is a naked single; the second is a hidden single.
There is no guarantee that the next useful move sits nearby. This is simply a bounded first check. If the changed area yields nothing, return to another digit or another house rather than assuming the previous move must immediately unlock an answer.
Write down uncertainty when it helps
If you keep revisiting the same three possible cells, write the restriction down. Notes can preserve that result while you inspect something else. There is no rule requiring an entire puzzle to be scanned without notation first.
Marking 7s only is different from listing every candidate in a cell. A cell containing one written 7 may still allow several other digits. Before using a naked-single or naked-pair argument, calculate the complete candidate lists needed for that argument.
You can also reverse the search. Pick a nearly complete row, list its missing digits, and test their positions against columns and boxes. Changing from digit-first to house-first inspection changes what is easy to notice without changing the rules.
Check the scope of every exclusion
A placed digit excludes itself from its peers; it does not block an entire remote box. Trace the actual row or column into the box you are inspecting. In our example, the 7 at r4c1 blocks column 1, but it says nothing directly about r3c2.
Do not use an unresolved candidate as though it were a placed digit. A note saying 7 might be at r4c1 cannot yet exclude 7 from r3c1. Only a proved location, or a separate argument covering all alternatives, provides that restriction.
Use the quiz to reconstruct the two diagrams. Then take one digit on a Standard board and explain each location you exclude. End the pass by stating the result precisely: one forced cell, several surviving cells, or no new information.
Go to the evidence
Sources & further reading
Research checked on 14 October 2026. Follow the original sources to explore the evidence and its limits.
- Conceptis — Sudoku techniques
Publisher explanations of scanning, candidate notation and elementary eliminations.
- Bernhard Hobiger — HoDoKu: Singles
Definitions of full houses, naked singles and hidden singles, with a discussion of scanning.
- Andrew Stuart — Getting Started
The solver author's introduction to forced placements; our examples are independently constructed.
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