The Intersection (Pointing) strategy, often called Pointing Pairs or Pointing Triples, is one of the most satisfying "Aha!" moments in Sudoku. It’s the first step in moving beyond just looking for empty spots and starting to use logic to eliminate possibilities.
A Pointing Pair occurs when you look into a single box and realize that a candidate number can only fit into one row or one column within that box. Because that number must appear in that line to satisfy the box, it effectively "points" across the rest of the grid, acting like a barrier for that entire line.
Interactive Example
Click "Apply Logic" to see the strategy in action.
Real Example Explanation
In the interactive example above, look at the Middle-Left Box (Box 3):
- Scan the Box: Look at the candidates for number 1 inside this 3x3 box.
- Find the Line: Notice that the number 1 can only appear in the cells highlighted in Green (R4C2 and R5C2).
- The Observation: These cells form a perfect vertical line inside Column 2.
- The Pointing: Since the number 1 must be in one of these two spots for this box, it "points" down the rest of the column.
- The Cleanup: We can eliminate number 1 from any other cell in Column 2 (shown in Red) because the box has already "claimed" the 1 for that column section.
How the Logic Works
This strategy allows you to remove candidates by spotting a local restriction that has a global impact.
- Focus on one box: Pick any 3x3 box.
- Find a candidate: Look for a number (e.g., X) and see where it can possibly go.
- The Alignment: If all the possible spots for X in that box are engaged in a single row (or column), then the X for that box is locked in that line.
- The Elimination: Since that line inside the box MUST contain the X, no other cell in that entire line (outside the box) can contain an X.
How to Spot Them Quickly
Scanning for Pointing Pairs is easier if you follow these habits:
- The "Cross-Cut" Method: When two columns already have a specific number (like 9), look at the third column. In the box where the 9 is missing, if the only open spots for 9 form a line, you’ve found a Pointing Pair.
- Pencil Marks are Key: This strategy is much easier to see if you use small "candidate" numbers in the corners of the cells. If you see a number appearing only in one line within a box, it’s a "pointer."
- Box → Line: Always remember the direction. Pointing is Box to Line. You find the restriction in the box first, then use it to clear the row or column. This is the exact opposite of Box/Line Reduction, where a restriction in a line claims a box. Here, a restriction in a box points to a line.
By clearing those extra candidates out of the row or column, you often "break" a stalemate in a completely different box, revealing a Hidden Single (the only place a number can go) or unwrapping a tricky Naked Pair.