Pointing Pairs: Eliminating Candidates Across Boxes
A Pointing Pair is a foundational Sudoku technique where all candidate positions for a specific digit within a single 3x3 box are confined to a single row or column. This alignment forces the digit to be placed somewhere in that line segment inside the box, which means it cannot appear anywhere else in the extended row or column outside the box. This powerful constraint allows you to make immediate eliminations and is a core example of a locked candidate strategy. Mastering this pattern is a critical step toward solving more challenging puzzles.
What Is a Pointing Pair?
A Pointing Pair is a specific pattern of candidate digits within a single 3x3 box. It occurs when, for a particular digit, all possible positions within that box are located in the same row or the same column. You can think of it as the digit being 'pointed' in one direction, locking its eventual placement to that line segment inside the box. This is a type of locked candidate technique, often called Box-Line Reduction because you reduce candidates in a line based on their confinement to a box. The classic visual is a box where, for example, the only two cells that can contain a '5' are both in the top row of that box.
How to Spot a Pointing Pair
To find a Pointing Pair, you systematically scan each 3x3 box, one candidate digit at a time. First, pick a box and a digit from 1 to 9. Scan all empty cells in that box and note every cell where that digit is a possible candidate. If all these candidate cells line up perfectly in a single row or a single column, you have found a Pointing Pair. It doesn't matter if there are two, three, or more candidate cells. The key is their alignment. This pattern is easier to spot after you have filled in basic pencil marks. Our hint engine frequently identifies this as the next logical step in puzzles where simple singles have been exhausted.
- Focus on one box and one digit at a time.
- Look for alignment. If the candidate cells are scattered in different rows and columns, it's not a Pointing Pair.
The Elimination Rule: How It Works
Once you confirm a Pointing Pair, you can make powerful eliminations. Because the digit must be placed within that aligned row or column segment inside the box, it is impossible for that same digit to appear anywhere else in the rest of that row or column. You can therefore erase that candidate digit from all other cells in the intersecting row or column that lie outside the 3x3 box. This often clears the way for other techniques, like revealing a Naked Single or creating a Naked Pair in another part of the grid. The elimination is absolute and is a direct consequence of Sudoku's basic row, column, and box rules.
Understanding Pointing Triples
A Pointing Triple follows the exact same logic as a Pointing Pair. The name simply indicates that three cells within a box are the only candidates for a digit, and they are all aligned in one row or column. The technique is still officially a form of Box-Line Reduction. Don't be confused by the name. Whether you have two, three, or even four aligned candidates (though four is very rare), the principle is the same: the digit is locked to that line within the box, and you eliminate it from the same line outside the box. The core action is always elimination based on confinement.
Connection to Box-Line Reduction
Pointing Pairs and its sibling strategy, Claiming Pairs/Triples, are the two subtypes of the broader strategy known as Box-Line Reduction. While a Pointing Pair locks a digit to a line *within* a box, a Claiming Pair locks a digit to a box *within* a line. Both techniques use the same core principle: if all candidates for a digit in a line are confined to one box, or all candidates in a box are confined to one line, you can make eliminations in the intersecting region. Understanding this relationship helps you see the puzzle as a connected system of constraints, which is essential for advancing to more complex methods.
Key Facts
- ▪A Pointing Pair occurs when all candidate cells for a digit within a 3x3 box lie in the same row or column.
- ▪The pattern gets its name because the aligned candidates 'point' along a row or column, restricting the digit's placement.
- ▪Once identified, you must eliminate that candidate digit from the rest of the intersecting row or column outside the box.
- ▪This technique is a specific type of locked candidate strategy, also known as Box-Line Reduction.
- ▪The pattern can involve more than two cells; three aligned candidates is called a Pointing Triple and works the same way.
- ▪Pointing Pairs are an intermediate technique, often used after filling in basic pencil marks and solving obvious singles.
- ▪Spotting a Pointing Pair often creates new opportunities to apply simpler techniques like Naked Singles or Naked Pairs.
- ▪The logic is absolute and derived directly from Sudoku's fundamental rules: each digit must appear once per row, column, and box.
Frequently Asked Questions
What's the difference between a Pointing Pair and a Naked Pair?
A Naked Pair involves two cells in a row, column, or box sharing the same two candidates. A Pointing Pair involves one digit whose candidates in a box align in one row/column, allowing elimination in the rest of that line.
Can a Pointing Pair exist in a column?
Yes. A Pointing Pair is defined by alignment within a box. If all candidates for a digit in a box are in one column, it's a vertical Pointing Pair. The elimination applies to the rest of that column outside the box.
Is a Pointing Triple a different technique?
No. A Pointing Triple uses the same logic as a Pointing Pair. The name just indicates three aligned candidate cells instead of two. Both are forms of Box-Line Reduction.
When should I look for Pointing Pairs?
Look for them after solving all obvious singles and filling in pencil marks. Scan each box systematically for each digit to see if its candidates are confined to a single row or column.
What happens after I make the elimination?
The elimination may reveal a Naked Single in another cell, complete a row or column, or create a new Naked Pair. Always re-scan the affected areas for new simple placements.