Pointing Pairs: Box-Line Intersections

Pointing Pairs (also called Box-Line Reduction) is an elegant technique that exploits the relationship between boxes and rows/columns.

What is a Pointing Pair?

A pointing pair occurs when a candidate number in a box can only appear in one row or column within that box. This "points" to where the number must go, allowing you to eliminate it from the rest of that row or column outside the box.

The Core Concept

If all candidates for a specific number in a box are confined to a single row or column, then that number must go somewhere in that row/column intersection. Therefore, you can eliminate that candidate from the rest of the row/column outside the box.

Example Scenario

Imagine Box 1 (top-left) where the number 6 can only appear in:

• Row 1, columns 1, 2, or 3

Since 6 must be in row 1 within this box, you can eliminate 6 from:

• Row 1, columns 4-9 (outside the box)

Why It's Called "Pointing"

The candidates "point" from the box toward a specific line (row or column), indicating where the number must be within that box.

How to Find Pointing Pairs

1. Pick a box (any of the nine 3x3 regions)
2. Choose a number that's missing from that box
3. Mark where it could go within the box
4. Check if all candidates are in one row or column
5. If yes: Eliminate that number from the rest of that row/column

The Two Variations

Pointing Row

All candidates for a number in a box line up in the same row → Eliminate from the rest of that row

Pointing Column

All candidates for a number in a box line up in the same column → Eliminate from the rest of that column

Common Mistakes

• Forgetting to eliminate: Finding the pointing pair is useless without the elimination step
• Eliminating from the wrong region: Only eliminate from outside the box, not inside it
• Missing the alignment: Make sure ALL candidates for that number in the box are in the same line
• Confusing with naked pairs: This is about number placement within boxes, not candidate pairs

Reverse Technique: Box-Line Reduction

The reverse also works! If a number in a row or column can only fit in one box, eliminate it from the rest of that box. This is sometimes called "claiming" or "box-line reduction."

Scanning Strategy

Systematic Approach:

1. Go through each box (1-9)
2. For each missing number, mark possible positions
3. If aligned in one row/column, eliminate from that line
4. Repeat for all boxes

Quick Scan:

• Look for boxes with many filled cells
• These often have pointing pairs for remaining numbers

Impact on Solving

Pointing pairs are especially powerful because:

• They bridge the box and line constraints
• Often unlock hidden singles
• Work on puzzles where basic techniques get stuck
• Can be found quickly with practice

Practice Tips

1. Start with boxes that have 6-7 numbers already filled
2. Visual scanning works better than tracking candidates
3. Check both rows and columns within each box
4. Don't forget to actually eliminate after finding the pattern!

Next Steps

After mastering pointing pairs, explore:

• Box-Line Reduction - The reverse of pointing pairs
• Naked Triples - Extending naked pairs to three cells
• Hidden Pairs - Finding less obvious pair patterns