Locked candidates: pointing pairs and box-line reduction
When a digit is confined to one line inside a box, use that overlap to remove candidates. Learn both directions with a concrete example.
One digit, two overlapping regions
Locked candidates use the overlap between a 3×3 box and a row or column. If every possible position for a digit in one region lies within the overlap, the digit cannot appear in the rest of the other region.
This is a statement about all possible positions for one digit. Other candidates in those cells do not matter. Start with accurate notes so that an unmarked possibility cannot invalidate the deduction.
Pointing: from a box to a line
Look at the top-left box, rows 1–3 and columns 1–3. Suppose its only positions for 7 are r2c1 and r2c3. Both are in row 2. The box must contain a 7, so row 2’s 7 must be inside that box.
Remove 7 from r2c4 through r2c9 wherever it is still a candidate. You cannot yet decide whether r2c1 or r2c3 is 7.
| Region | Possible positions for 7 | Conclusion |
|---|---|---|
| Top-left box | r2c1, r2c3 | 7 lies in row 2 |
| Row 2 outside that box | r2c4 … r2c9 | Remove candidate 7 |
Claiming: from a line to a box
Now reverse the premise. Suppose the only possible positions for 7 in row 2 are r2c1 and r2c3. Since both are in the top-left box, that box’s 7 must lie in row 2. Remove candidate 7 from the box’s cells in rows 1 and 3.
This direction is often called claiming or box-line reduction. The name varies between guides. The dependable distinction is the source region you checked completely and the target region from which you remove candidates.
Two positions are not a requirement
Three candidate positions all in one row inside a box produce the same deduction, often called a pointing triple. If just one position remains in the source region, you have a hidden single and can place the digit directly.
If the top-left box also permits 7 at r3c2, the pointing example fails: its 7 could lie in row 3. Check every empty cell in the source region, not only the two that first caught your eye.
Try it with a column
The logic is identical after rotating the example.
In the bottom-right box, digit 5 can appear only at r7c8 and r9c8. Where outside that box can you remove candidate 5?
Show the explanation
From column 8 in rows 1–6. The box’s 5 must occupy column 8, so no other 5 fits in that column. Neither r7c8 nor r9c8 is individually solved yet.
What to inspect next
After an elimination, check the affected cells for naked singles and their regions for hidden singles. One removed note can create a forced move even when the two pointing cells stay unchanged.
When recording the step, name the digit, source region and eliminated positions. “7 is locked to row 2 inside box 1” is easier to verify than simply calling a pattern a pair.