If you’ve ever found yourself staring at a Sudoku grid where the obvious "single" numbers have run out, you’ve likely reached the point where you need to look at Intersections.
Also known as Box/Line Reduction or Claiming, this strategy is the bridge between beginner scanning and expert logic. It works by removing "pencil marks" (candidates) to reveal Hidden Singles or Naked Pairs elsewhere.
Interactive Example
Click "Apply Logic" to see the strategy in action.
Real Example Explanation
In the interactive example above, we are looking at Row 1 (the second row from the top):
- Scan the Row: When we check the possible spots for the number 3, we see it can only go in two cells: R1C6 and R1C8 (highlighted in Green).
- Check the Box: Both of these cells are inside the Top-Right Box (Box 2).
- The Conclusion: The 3 for Row 1 must be in one of those two spots. Therefore, the Top-Right Box must get its 3 from Row 1.
- The Cleanup: We can eliminate the number 3 from any other cell in the Top-Right Box (highlighted in Red). This clears up the board for further logical steps.
The Core Concept
Sudoku is a game of constraints. Each number must exist in a row, a column, and a 3x3 box. The Intersection strategy works because these areas overlap.
The logic is simple: If a number must go in a specific part of a row (or column), and that part is entirely contained within one 3x3 box, then that number cannot appear anywhere else in that box.
This is commonly called Claiming (or the "Line to Box" move).
How "Claiming" Works
- Scan a Line: Look at a single row or column.
- Find a Restriction: Notice that for a specific number (e.g., 7), the only available spots in that row are all confined within a single 3x3 box.
- The Logic: Since that row needs a 7, and it must go in that specific box, the row "claims" the 7 for that box.
- The Elimination: You can safely remove 7 from all other cells in that box that are not part of your row.
What about the Reverse? (Pointing Pairs)
There is a sister strategy called Pointing Pairs (or the "Box to Line" move).
- Pointing: You look at a Box first. If a number is restricted to a single row within that box, it points outward. You eliminate that number from the rest of the row outside the box.
- Claiming (This Strategy): You look at a Row first. If a number is restricted to a single box, it claims the box. You eliminate that number from the rest of the box outside the row.
Both rely on the exact same logic—just viewed from different directions.
Pro Tip for Spotting It
Don't try to look at the whole board at once.
- Pick a Number: Start with '1' and assume you are looking for it.
- Scan Lines: Move down row by row.
- Check Grouping: If you see that all potential '1's in a row are bunched together in one box, you've found an Intersection!