Hidden Unique Rectangle

Level 8 · Blue Belt

Strategy:

Unique Rectangles

Requires:

Unique Rectangle Type 1

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

Look for Hidden Unique Rectangle.

1

Hidden Unique Rectangle

Cells r2c1, r2c4, r1c1, and r1c4 form a rectangle across 2 boxes with candidates 5 and 7.

2

Hidden Unique Rectangle

Floor cells r2c1 and r2c4 are bivalue { 5, 7 }, creating part of a deadly pattern.

3

Hidden Unique Rectangle

Digit 5 is hidden in the roof cells' shared house — it only appears at r1c1 and r1c4.

4

Hidden Unique Rectangle

That leaves 7 as the removable roof candidate in r1c1 and r1c4.

5

Hidden Unique Rectangle

To avoid the deadly pattern, eliminate 7 from r1c1 and r1c4.

6

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.