Hidden Unique Rectangle

Level 9 · Purple Belt

Strategy:

Unique Rectangles

Overview

Hidden Unique Rectangle identifies a deadly pattern where the UR digit is 'hidden' in the roof cells' shared house. If the digit appears only in the roof cells within that house, it can be eliminated to prevent the deadly pattern.

How It Works

  1. Find a potential deadly rectangle with floor cells containing only {X,Y}.
  2. Identify the roof cells' shared house (row, column, or block).
  3. Check if one UR digit appears in that house only at the roof cells.
  4. That digit is 'hidden' - eliminate it from the roof cells to prevent the deadly pattern.

Example

Starting position

Look for Hidden Unique Rectangle.

1

Rectangle with 1 and 6

Cells r5c2, r9c2, r5c3, and r9c3 form a rectangle across 2 boxes with candidates 1 and 6.

2

Bivalue floor cells r5c2 and r9c2

Floor cells r5c2 and r9c2 are bivalue { 1, 6 }, forming part of a two-solution rectangle.

3

1 is hidden in the roof house

Digit 1 is hidden in the roof cells' shared house: it appears only at r5c3 and r9c3.

4

6 is the removable roof candidate

That leaves 6 as the removable roof candidate in r5c3 and r9c3.

5

Remove 6 from the roof cells

To avoid the two-solution rectangle, remove 6 from r5c3 and r9c3.

6

Result

Result after applying the technique.

Tips & Patterns

  • Hidden URs are harder to spot than standard URs because the key digit is hidden among other candidates.
  • Focus on the roof cells' shared house and check for digits confined to just those cells.
  • The technique relies on uniqueness assumption.