Unique Rectangle Type 2

Level 5 · Orange Belt

Strategy:

Unique Rectangles

Requires:

Unique Rectangle Type 1

Overview

Unique Rectangle Type 2 is similar to Type 1, but two cells (on the same side) share an additional candidate. That extra candidate must be placed in one of them, so it can be eliminated elsewhere.

How It Works

  1. Find a potential deadly pattern rectangle with candidates {X,Y}.
  2. Two cells on the same side have one additional candidate Z (same in both).
  3. Z must be placed in one of these cells to avoid the deadly pattern.
  4. Eliminate Z from cells that see both of these "roof" cells.

Example

Starting position

Look for Unique Rectangle Type 2.

1

Find a rectangle on 1 and 5

Find four cells forming a rectangle across 2 boxes. Two cells have only { 1, 5 }.

2

Roof cells share extra candidate 2

The other two cells (r7c7 and r9c7) have { 1, 5 } plus extra candidate 2.

3

One roof cell must be 2

To avoid the two-solution rectangle, one of these cells must be 2, not 1 or 5.

4

Common peers of the roof cannot keep 2

Any cell that sees both roof cells would then see that forced 2, so those highlighted cells cannot keep 2.

5

Remove 2 from cells seeing both roofs

Remove 2 from cells seeing both r7c7 and r9c7: r4c7 and r9c8.

6

Result

Result after applying the technique.

Tips & Patterns

  • The two cells with extra candidates must be in the same row or column (not diagonal).
  • The extra candidate Z is the same in both cells.
  • Type 2 makes eliminations outside the rectangle.