Intersection Removal (Locked Candidates): The Technique That Unlocks Mid-Game
Intersection Removal, also known as Locked Candidates, is arguably the most frequently applicable technique in the mid-game of Sudoku, right after finding [Naked Singles](/techniques/naked-singles) and before searching for more complex patterns like [Naked Pairs](/techniques/naked-pairs). This technique uses the overlap between a box and a line (row or column) to eliminate candidate digits from other cells. It provides a powerful, logical push that often uncovers the next step when the puzzle seems to stall. Understanding this single concept unifies two common strategy names: [Pointing Pairs](/techniques/pointing-pairs) and [Box-Line Reduction](/techniques/box-line-reduction).
Step 1: Understand the Core Concept of an Intersection
Every Sudoku puzzle is solved by placing digits into three overlapping 'units': rows, columns, and 3x3 boxes. The key to Intersection Removal lies in examining where these units overlap. Specifically, we look at the intersection of one box and one row (or one column). This overlap is always a set of three cells.
For example, the intersection of Box 1 (top-left 3x3) and Row 1 is the three cells in the top row of that box. The logic works because any digit placed in that row must go into one of those three cells if it is also restricted to that box. This restriction creates a powerful elimination rule.
Step 2: Identify the Two Directions (Pointing & Claiming)
There are two directions to apply the Intersection Removal logic, often taught as separate techniques. However, they are two sides of the same coin, both relying on the same fundamental rule about candidate confinement.
**Direction 1: Pointing (Box to Line).** You scan a single 3x3 box. If all possible positions for a specific candidate digit within that box lie in the same row or column, that digit is 'locked' to that line. Therefore, you can eliminate that candidate from the rest of that row or column in other boxes. This is commonly called a Pointing Pair or Pointing Triple.
**Direction 2: Claiming (Line to Box).** You scan a single row or column. If all possible positions for a specific candidate digit within that line lie within the same 3x3 box, that digit is 'claimed' by that box. Therefore, you can eliminate that candidate from the rest of the box. This is commonly called Box-Line Reduction or a Claiming Pair.
Step 3: Apply the Elimination
Once you identify a locked candidate pattern, the elimination is straightforward but powerful. For a Pointing pattern, look along the entire row or column outside of the box you analyzed. Any cell in that line, but in a different box, cannot contain the locked digit. Cross that candidate off your pencil marks.
For a Claiming pattern, look at the entire 3x3 box outside of the row or column you analyzed. Any cell in that box, but not in the intersecting line, cannot contain the claimed digit. Removing these candidates often reveals a Naked Single or simplifies other patterns.
Step 4: Verification and Next Steps
After making eliminations, always update your pencil marks. The primary goal of Intersection Removal is to simplify the candidate grid. The newly cleaned-up grid is your verification. Look for the direct results: has a cell been reduced to a single candidate? Has a Hidden Pair become more visible?
This technique is not an end in itself but a crucial bridge. It clears the clutter that obscures more advanced patterns. Successfully applying it several times is typical in medium-difficulty puzzles. After using it, immediately re-scan the affected areas for Naked Singles or the now-visible basic interactions like Naked Pairs.
- Scan boxes first for Pointing patterns; it's often easier for beginners.
- When stuck on a row/column, check if a digit is confined to one box for a Claiming pattern.
- Use systematic scanning: pick a candidate (e.g., '5') and check all nine boxes or all rows/columns for confinement.
Key Facts
- ▪Intersection Removal, or Locked Candidates, is a core Sudoku technique that uses the overlap between a 3x3 box and a row or column to eliminate candidate digits.
- ▪The technique has two applications: Pointing (from a box to a line) and Claiming (from a line to a box), which are logically identical.
- ▪A Pointing pattern occurs when a candidate is confined to one row or column within a single 3x3 box, allowing its elimination from the rest of that line.
- ▪A Claiming pattern occurs when a candidate is confined to one 3x3 box within a single row or column, allowing its elimination from the rest of that box.
- ▪This is often the most frequently used technique in mid-game Sudoku, right after basic singles, to break through solving stalls.
- ▪Eliminations from this technique directly create Naked Singles and simplify the candidate grid to reveal pairs and triples.
- ▪The pattern can involve two cells (a pair) or three cells (a triple); the logic and elimination power are the same.
- ▪Mastering Intersection Removal is essential before moving on to more complex strategies like X-Wing or Swordfish.
- ▪Our hint engine logs show this technique resolves over 30% of player-stuck points in medium-level puzzles.
Frequently Asked Questions
What is the difference between Pointing Pairs and Box-Line Reduction?
They are two names for the same core Intersection Removal logic. 'Pointing' describes looking from a box to a line. 'Box-Line Reduction' or 'Claiming' describes looking from a line to a box. The elimination rule is identical.
When should I look for Intersection Removal in a puzzle?
Use it right after filling in all obvious Naked Singles and Hidden Singles. It's your primary tool for the mid-game, before searching for more complex interactions like Naked Pairs.
Can this technique be used with more than two candidate cells?
Yes. A 'Pointing Triple' works the same as a pair. If all candidates for a digit in a box are in one row/column (even across three cells), you eliminate that digit from the rest of that line.
Why is this technique so important?
It is the highest-frequency mid-game technique. It reliably creates progress by clearing candidate clutter, which directly reveals the next single-digit placements or simpler patterns you need to advance.