Lesson:Pointing Pairs
When a candidate in a 3x3 box is restricted to a single row or column...
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Pointing Pairs (also called Pointing Doubles or Locked Candidates Type 1) is an intersection technique that exploits the relationship between a 3×3 box and its intersecting rows and columns. It is one of the most commonly applicable intermediate techniques and is usually the first intersection method solvers learn after mastering Naked and Hidden Singles.
A Pointing Pair occurs when a specific candidate digit, within a given 3×3 box, can only appear in two (or three — then called a Pointing Triple) cells, and all those cells happen to lie in the same row or the same column. Since the digit must go somewhere in the box, and all possible positions align on one line, the digit is "locked" to that line within the box. Consequently, it cannot appear in any other cell along that same line outside the box.
Pointing Pairs are particularly effective when rows or columns have several candidates and scanning alone cannot determine placements. By eliminating a candidate from even one cell outside the box, you may uncover a Hidden Single or reduce a cell to a Naked Single.
How It Works — Step by Step
Step 1 — Select a box and a digit
Choose a 3×3 box and a digit that has not been placed there yet. Find every empty cell in the box where the digit is still a legal candidate.
Step 2 — Check if all positions align on one line
If the candidate positions (two or three cells) all lie in the same row — that is, all share the same row number — you have a row-based Pointing Pair (or Triple). If they all share the same column number, you have a column-based Pointing Pair.
Step 3 — Eliminate from the rest of that line
In the identified row or column, the digit must be placed within the box (since only those cells in the box allow it). Therefore, eliminate the digit from every other cell in that row or column that belongs to a different box.
Step 4 — Look for new singles
Re-examine the affected row or column and the boxes it intersects. Eliminations from Pointing Pairs frequently reveal Hidden Singles or Naked Singles in the neighboring boxes.
When to Use This Technique
Use Pointing Pairs after exhausting Naked and Hidden Singles. They are a standard part of the solving toolkit for Medium and Hard puzzles. Always check every box for locked candidates as part of your systematic candidate-elimination routine.
Worked Examples
In the top-center 3×3 box, digit 4 can only legally appear in Row 1, Column 5 and Row 1, Column 6. Both cells are in Row 1. By Pointing Pairs, digit 4 cannot appear anywhere else in Row 1. Remove 4 from R1C1, R1C2, R1C3 (top-left box cells) and R1C7, R1C8, R1C9 (top-right box cells). If R1C7 had {4, 8} as candidates, it now has only {8} — a Naked Single!
Frequently Asked Questions
What is a Pointing Triple?
A Pointing Triple is the same as a Pointing Pair but involves three cells all in the same line within a box. The logic is identical — eliminate the digit from the rest of that line.
Can a Pointing Pair affect a column and a box simultaneously?
Only if the two Pointing Pair cells share both the same row/column AND the same box — which they always do by definition. The elimination only applies to the line (row or column), not to other parts of the box.
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