Block and Column/Row Interaction: Locked Candidates Explained

Understanding Block and Column/Row Interaction

At its core, block and column/row interaction relies on the basic Sudoku rule: a digit must appear exactly once in every row, column, and 3x3 box. This technique focuses on the intersection where a box meets a row or column. When all possible placements for a specific digit within a single 3x3 box lie on the same row or column, that digit is 'locked' into that line for that particular box. Because the digit must be placed somewhere in that line within the box, it cannot appear elsewhere in the same line outside the box. This logical deduction is the foundation of Box-Line Reduction.

Our hint engine finds that players often miss this pattern because they scan boxes, rows, and columns in isolation. The key is to look for the relationship between them. When you spot a candidate digit appearing only in one row or column of a box, even if it appears in multiple cells along that line, you have identified a powerful elimination opportunity. This specific pattern is often called a Pointing Pair or pointing triple when two or three cells are involved.

• Focus on one candidate number at a time. Scan each 3x3 box to see where that number can possibly go.
• If all possible cells for that number in a box are in the same row, the number is 'locked' to that row within the box.
• You can then erase that candidate number from the rest of that row, but only in the cells outside the original box.

Step-by-Step: The First Direction (Pointing)

This first and most common form of the technique involves a digit being confined within a box. Let's walk through the numbered steps. First, choose a candidate digit and a single 3x3 box. Examine all nine cells of that box. If the digit you are analyzing can only be placed in cells that all share the same row or the same column, you have completed step one: finding a digit confined to one line inside a box.

For step two, trace that entire row or column outside of the box you just examined. In every other cell along that line that is not within your original box, you can safely eliminate the candidate digit. This is because placing the digit in any of those external cells would violate the rule, as the box would then have no valid place for that digit. This elimination is the essence of Box-Line Reduction.

For example, imagine in a box, the candidate '5' only appears in the top row, occupying two cells. The '5' for this box must be placed in one of those two cells. Therefore, a '5' cannot be placed anywhere else in that top row in the two adjacent boxes. You would remove '5' as a candidate from all other cells in that row.

The Reverse Direction: Claiming

The interaction also works powerfully in the reverse direction, sometimes called 'Claiming' or 'Locked Candidates Type 2'. Here, the logic starts with a row or column instead of a box. In this case, you find a candidate digit that, within a specific row or column, can only be placed inside one particular 3x3 box.

When this happens, that digit is effectively 'claimed' by that box for that row or column. Since the digit must be placed somewhere in that line, and its only options are within a single box, you can eliminate that candidate digit from all other cells within that same box. This clears out false possibilities and often directly reveals the final placement. This is a crucial form of Intersection Removal.

For instance, if in a given row, the candidate '3' appears only in three cells, and all three of those cells are inside the same 3x3 box, then the '3' for that row must be placed within that box. Consequently, you can remove '3' from every other cell in that 3x3 box, even those not in the original row. This often simplifies the box dramatically, leading to new Naked Singles or other patterns.

Why This Technique is Essential

Block and column/row interaction is not an advanced trick, it is a fundamental logical step. Most standard Sudoku puzzles beyond the easiest levels require its application to proceed. Without spotting these locked candidates, your pencil marks become cluttered with impossible options, making it very difficult to see simpler techniques like Hidden Pairs or X-Wings.

The technique is efficient because it often creates a cascade of new information. A single elimination from a pointing pair might reveal a hidden single in a row. A claiming elimination might create a naked single in a box. Our data shows that puzzles rated as 'Medium' difficulty typically have 2-4 applications of this technique. Mastering it significantly reduces your solve time and reliance on guessing.

• Practice by focusing on puzzles labeled 'Medium'. Slow down and consciously look for locked candidates on digits 1 through 9.
• Use pencil marks! This technique is nearly impossible to spot without noting all possible candidates in each cell.
• After making eliminations, always rescan the affected areas. New placements or simpler techniques often appear immediately.