How to Master Unique Rectangle Type 3 in Sudoku

When extra candidates spill into two corners of a rectangle in different combinations, simple elimination isn’t enough. The Unique Rectangle Type 3 technique solves this by combining the uniqueness rule with traditional subset strategies.

This technique combines the Unique Rectangle with the “Naked” \ “Hidden” techniques.

Identifying Unique Rectangle Type 3

Look for four cells forming a rectangle across two 3×3 blocks, two rows, and two columns:

• Two Pure Corner Cells: Contain strictly the base pair (1 and 5),
• Two Modified Corner Cells: Contain the base pair plus extra candidates.

If you look at the example you’ll see that two cells in the Unique Rectangle have extra candidates: 4, 6 and 6, 9.

This means that the values 4, 6, and 9 are the candidates for these two cells.

The Logic: Forming a Naked Subset

To prevent a Deadly Pattern, the extra candidates in those two modified corners must act as a single pseudo-cell unit for the grid. Because these two corners share a line (a row or a column), their extra candidates join forces with other empty cells along that same line.

This forms a Naked Triplet pattern when combined with the two cells in the same column that also contain the values 4, 6, and 9.

Because the combined pool of candidates across these aligned cells is restricted to exactly three digits (4, 6, and 9), those numbers are mathematically locked into those specific spots.

The Elimination Rule

Once the Naked Subset (Pair, Triple, or Quad) is established along the shared line or within the shared 3×3 block, you can treat it like a standard subset elimination.

Therefore, 4, 6, and 9 cannot be placed in any other cell in the column.

📍 Steps to Clean the Grid:

1. Identify the Extra Candidate Pool: Combine the non-base candidates from the two modified corners of your Unique Rectangle.
2. Find the Matching Subset: Scan the shared row, column, or block for additional cells that contain only those same extra digits.
3. Purge the Line: Delete those subset numbers (4, 6, and 9) from the pencil notes of every other cell in that line or block.

Mastering Advanced Sudoku Syntheses

Unique Rectangle Type 3 is one of the most satisfying techniques to execute because it bridges two completely different solving philosophies. Recognizing how a potential Deadly Pattern converts into a Naked Subset lets you clear locked notes across entire rows and columns in one move.

Ready to combine your solving techniques? Put your logic to the test right now on our Sudoku Puzzles, keep your pencil notes active, and look for those powerful subset intersections!