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

In the bottom-left box the digit 1 survives only in r7c1 and r8c1, both in column 1. The solver therefore erases 1 from r3c1.
c1c2c3c4c5c6c7c8c9
r1914568315678156714568457845782
r245845682356789356794568945789457891
r314581458715891592458936
r4478489615789157931457892578
r52378891256789456893578957893578
r62347848951278912791891347896378
r71583891256912569156912567815784
r8157412356815612356159
r962894135971358158358
Pattern cells
r7c1, r8c1
Eliminations
1 from r3c1

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

  1. 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.
  2. 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.
  3. 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.
  4. 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

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.