Pointing Pair Sudoku Technique
Updated
A pointing pair occurs when a digit can only go in two cells of a box and both of those cells lie on the same row or column, so the digit can be erased from every other cell of that line.
When a pointing pair applies
A pointing pair is the first technique on this list that never places a digit. It removes candidates, and those removals are what make the next single visible. The logic is short: every box contains each digit exactly once, so if a digit has only two possible cells left in a box and both share a row, the digit is definitely in that row. Anything else on the row, outside the box, can therefore lose the candidate.
The technique is also known as a locked candidate or box-line interaction of type one. The direction matters: a pointing pair reasons from the box outward to the line. The reverse deduction, from a line inward to a box, is box line reduction and is listed separately.
Pointing pairs are extremely common in medium puzzles. They usually appear the moment a box loses most of its blanks, because the surviving candidates for a digit get squeezed into a single band of three cells.
Worked example
The bottom-left box has four empty cells: r7c1, r7c3, r8c1 and r9c3. Only r7c1 and r8c1 can still take a 1, and they sit one above the other in column 1. Whichever of the two ends up holding the digit, column 1 gets its 1 from inside that box.
Column 1 has one other cell that still listed 1 as a candidate, r3c1, and it is now impossible. Removing it leaves r3c1 with 4, 5 and 8. Nothing was placed, but the column is one step closer to a single, which is exactly what an intersection technique is for.
How to spot a pointing pair
- Choose a box that is missing a digitWork box by box and pick a digit the box still needs. Boxes with three or four blanks give the best odds.
- Mark every cell in the box that can hold itCross out cells blocked by their row or column. You are looking for exactly two survivors.
- Check whether the two survivors share a lineBoth in the same row, or both in the same column, is what makes the pair point. Two cells sitting diagonally prove nothing.
- Erase the digit from the rest of that lineDelete the candidate from the six cells of the line that lie outside the box, then look for a naked or hidden single among them.
Common mistakes
- Erasing the candidate from the wrong direction, that is from the rest of the box instead of the rest of the line.
- Accepting two survivors that are not aligned. If the pair is diagonal inside the box, the digit is not locked to any line and there is nothing to remove.
- Forgetting that the two pair cells keep the candidate. A pointing pair says nothing about which of the two takes the digit.
- Skipping the follow-up scan. The elimination is only useful if you then look for the single it exposed.
Pointing pair FAQ
Is a pointing pair the same as a locked candidate?
Yes. “Locked candidate type 1” and “box-line interaction” are the same deduction. Suuudokuuu names it Pointing Pair when two cells are involved and Pointing Triple when three are.
Does a pointing pair ever place a digit?
Not by itself. It only removes candidates. Those removals frequently turn a nearby cell into a naked single or a digit into a hidden single, which is where the placement comes from.
What is the difference from box line reduction?
A pointing pair starts in a box and eliminates along a line. Box line reduction starts on a line and eliminates inside a box. Same intersection, opposite direction of reasoning.
Do I need full pencil marks to use it?
You need the candidates for one digit in one box, which is easy to work out by cross-hatching. Full pencil marks make the pattern obvious but are not required to find it.