Block/Block Interaction in Sudoku: Definition and Examples
Block/Block Interaction is a Sudoku candidate elimination technique where a digit is confined to a specific row or column segment in two aligned boxes, forcing its placement in the remaining segment of the third box in the same chute. This allows you to eliminate that candidate from the other rows or columns within that third box. For example, if the candidate 5 appears only in row 1 of box 1 and only in row 2 of box 2, then in box 3 (the third box in the top chute), the candidate 5 must be placed in the remaining row, which is row 3, and can be removed from rows 1 and 2 within box 3. This technique is a powerful form of [locked candidates](/techniques/locked-candidates) that operates across three boxes.
Understanding the Pattern and Logic
Block/Block Interaction occurs within a 'chute'—a set of three boxes aligned in a row (a band) or a column (a stack). The logic works because a single digit must appear exactly once in each row (for a band) or column (for a stack). If you find that the candidate for a specific digit is locked into one row in the first box and a different row in the second box of the same band, then the digit's position for the third box is forced: it cannot reuse the rows already occupied in the other two boxes. It must go into the one remaining row of that third box. Therefore, you can eliminate that candidate from the cells in the other two rows inside that third box. This is a key strategy in Sudoku Candidate Elimination.
A Concrete Walk-Through Example
Imagine the top band (boxes 1, 2, and 3). Let's trace candidate 7. In Box 1 (top-left), candidate 7 appears only in cells R1C1 and R1C2 (confined to row 1). In Box 2 (top-center), candidate 7 appears only in cells R2C4 and R2C5 (confined to row 2). This means in the top band, candidate 7 is locked into row 1 of Box 1 and row 2 of Box 2. Therefore, in Box 3 (top-right), the candidate 7 cannot be placed in its row 1 or row 2, as those rows are already 'claimed' for the digit 7 in this band. The only row left in Box 3 for the digit 7 is row 3. You can safely eliminate candidate 7 from all cells in rows 1 and 2 within Box 3 (specifically, from any cell in R1C7, R1C8, R1C9, R2C7, R2C8, or R2C9 that had 7 as a candidate).
- Always look for this pattern within a single band (three horizontal boxes) or stack (three vertical boxes).
- The candidate must be strictly confined to one row (or column) in each of the first two boxes. If it appears in two rows in one box, the pattern does not hold.
- The eliminations happen only in the third box, specifically from the rows or columns already 'used' by the candidate in the other two boxes.
How It Differs from Box-Line Reduction
Block/Block Interaction is often confused with Box-Line Reduction (also called Pointing Pairs/Triples or Claiming), but they are distinct. Box-Line Reduction involves a relationship between one box and one row or column. If a candidate in a box is confined to a single row, you can eliminate that candidate from the rest of that row outside the box. It's a two-entity interaction (box ↔ line). Block/Block Interaction is a three-entity interaction involving three boxes in the same chute. It requires analyzing how a candidate is locked in two boxes to deduce its forced row/column in the third box. You can learn more about the simpler technique in our Box-Line Reduction Guide. In practice, Box-Line Reduction is more common and should be looked for first. Block/Block Interaction is a more advanced, less frequent pattern that solves tougher puzzles.
When to Use Block/Block Interaction
This technique is a mid-to-advanced strategy. Use it when simpler methods like Pointing Pairs and Naked Pairs no longer yield progress. It becomes relevant in harder puzzles where candidates are more spread out. Scan each band and stack systematically. Look for a candidate that, in two of the three boxes, is completely confined to a single row (for a band) or column (for a stack). Crucially, the confined rows/columns in these two boxes must be different from each other. If you find this configuration, immediately look at the third box in that chute and perform the eliminations. Mastering this interaction is a significant step towards solving difficult Sudoku puzzles without guessing.
Key Facts
- ▪Block/Block Interaction is a Sudoku technique for eliminating candidates based on the alignment of a digit across three boxes in the same row band or column stack.
- ▪The pattern requires a candidate to be confined to one specific row in the first box and a different specific row in the second box of a band.
- ▪This confinement forces the candidate to occupy the only remaining row in the third box of that band, allowing eliminations from the other rows within that third box.
- ▪The same logic applies vertically: confinement to different columns in two boxes of a stack forces the candidate into the remaining column of the third stack box.
- ▪Eliminations occur only within the third box, specifically from the rows or columns that are already 'used' by the candidate in the aligned boxes.
- ▪This technique is a specific, advanced form of the broader 'Locked Candidates' strategy, which also includes the more common Box-Line Reduction.
- ▪Block/Block Interaction is distinct from Box-Line Reduction, which involves a direct interaction between one box and one row/column, not three boxes.
- ▪The technique is most useful in harder Sudoku puzzles where basic strategies have been exhausted and candidates are widely distributed.
Frequently Asked Questions
What is the main goal of Block/Block Interaction?
To eliminate candidate digits from specific cells in a Sudoku box by analyzing how that candidate is locked into rows or columns across two other boxes in the same band or stack.
Can Block/Block Interaction happen with boxes that are not adjacent?
Yes, but only if all three boxes are in the same chute (band or stack). The first and third box in a band can interact via the middle box. The key is the alignment across the entire group of three.
How is this different from a Pointing Pair?
A Pointing Pair (Box-Line Reduction) eliminates candidates outside a box. Block/Block Interaction eliminates candidates inside a box based on the configuration in two other boxes. The scope and direction of elimination are different.
Is this technique common in easy puzzles?
No. Block/Block Interaction is an advanced technique typically found in medium to hard puzzles. Easier puzzles are usually solved with simpler methods like singles, pairs, and basic Box-Line Reduction.
What's the first thing to check when looking for this pattern?
Scan each band and stack. For a candidate, check if it is confined to one row in two different boxes of that band. If the confined rows are different, you've found the pattern for a horizontal Block/Block Interaction.