Unique Loop Type 2 is an advanced "uniqueness" strategy that builds on the concept of Unique Loop Type 1. While Type 1 handles a single rescue cell, Type 2 handles multiple cells that share the same extra candidate.

This strategy uses the fundamental Sudoku rule: every valid puzzle has exactly one unique solution.

Real Example Walkthrough

In the example puzzle above, the solver identifies a 6-cell Unique Loop:

The Loop Cells:

The Analysis:

1. The loop pair: Most cells contain candidates {1, 7} or subsets that include these values
2. Three rescue cells: R3C4, R3C5, and R8C4 all have the same extra candidate: 4
3. The logic: At least ONE of these three cells must be 4 to break the deadly pattern
4. Common peer: R1C4 can see all three cells (same column as R3C4 and R8C4, same box as R3C4 and R3C5)
5. Elimination: Since one of {R3C4, R3C5, R8C4} must be 4, R1C4 cannot be 4

Result: Eliminate 4 from R1C4.

Understanding the Logic

What Makes Type 2 Different from Type 1?

In Type 1, we eliminate values from the rescue cell. In Type 2, we eliminate the extra value from other cells that can see all rescue cells.

Why Does This Work?

The loop would become a deadly pattern if all cells contained only the loop pair (e.g., {1, 7}). To prevent this:

• At least one rescue cell must take the extra value (4 in our example)
• If any cell outside the loop can "see" ALL rescue cells, that cell cannot contain the extra value
• Why? Because whoever ends up being 4 among the rescue cells would conflict with it!

Think of it as a "forced location" — the extra value must go in one of the rescue cells, so it cannot go anywhere that sees all of them.

Step-by-Step: How to Apply Type 2

1. Identify a Unique Loop: Find 4+ cells forming a closed loop with the same two candidates
2. Find rescue cells: Locate cells that have extra candidates beyond the loop pair
3. Check for shared extra: Do all rescue cells share the same extra candidate?
4. Find common peers: Which cells can see all the rescue cells?
5. Eliminate: Remove the shared extra from any common peer that contains it

Finding Common Peers

A common peer is a cell that shares a row, column, or box with every rescue cell.

In our example: - R3C4 is in Row 3, Column 4, Box 2 - R3C5 is in Row 3, Column 5, Box 2 - R8C4 is in Row 8, Column 4, Box 8

R1C4 is in Column 4, which is shared with R3C4 and R8C4. But wait—R3C5 is in Column 5, not 4!

Actually, R1C4 sees: - R3C4 via Column 4 ✓ - R8C4 via Column 4 ✓ - R3C5 via Box 2? No, R1C4 is in Box 2 (rows 1-3, columns 4-6), and R3C5 is also in Box 2 ✓

So R1C4 is a valid common peer through the combination of shared column and shared box.

Visual Pattern Recognition

Type 2 has a distinctive pattern:

``` Loop cells: ● (loop pair only) Rescue cells: ★ (loop pair + shared extra) Common peer: ✕ (can see all ★ cells)

 C4    C5    C6
┌─────┬─────┬─────┐

R1 │ ✕ │ │ │ ← Common peer (eliminate extra here) ├─────┼─────┼─────┤ R3 │ ★ │ ★ │ │ ← Rescue cells (both have extra 4) ├─────┼─────┼─────┤ R4 │ │ ● │ ● │ ← Regular loop cells ├─────┼─────┼─────┤ R8 │ ★ │ │ ● │ ← Mixed: rescue + regular └─────┴─────┴─────┘ ```

Common Misconceptions

"The rescue cells must all be adjacent"

No. Rescue cells can be anywhere in the loop. What matters is that they share the same extra candidate and have at least one common peer.

"I need exactly 2 rescue cells"

No. Type 2 works with 2 or more rescue cells, as long as they all share the same extra. Our example has 3 rescue cells!

"The elimination always happens in the loop"

No. Type 2 eliminates from cells outside the loop. The rescue cells keep their extra candidate — we're eliminating from their common peers.

Comparison Table

When Type 2 Doesn't Apply

• Different extras: If rescue cells have different extra candidates → Try Type 3
• No common peers: If no cell sees all rescue cells → No elimination possible
• Common peers lack the extra: If common peers don't have the extra value → No elimination possible

Tips for Beginners

1. Master Type 1 first: Understanding Unique Loop Type 1 makes Type 2 much easier
2. Focus on the extra: Once you find rescue cells, check if they share the same extra
3. Draw the connections: Mark which cells can see each rescue cell to find common peers
4. Use candidate notation: Clearly mark all candidates — shared extras become obvious
5. Check all regions: Common peers can share row, column, OR box with rescue cells

Why This Strategy Works

The uniqueness principle guarantees that a valid Sudoku has one and only one solution.

The loop creates a potential deadly pattern. The rescue cells prevent it by containing extra candidates. Since: - At least one rescue cell must become the extra value - The extra value must appear in exactly that location - Therefore, any cell seeing ALL rescue cells cannot contain the extra

It's a logical certainty — eliminating from common peers is guaranteed safe.

Related Strategies

Unique Loop Family

• Unique Loop Type 1 — Single rescue cell eliminates loop values
• Unique Loop Type 3 — Rescue cells' extras form a Naked Subset
• Unique Loop Type 4 — One loop value is locked to rescue cells

Unique Rectangle Family

• Unique Rectangle (Type 1) — 4-cell deadly pattern with single rescue
• Unique Rectangle (Type 2) — 4-cell version of this strategy
• Unique Rectangle (Type 3) — 4-cell with Naked Subset
• Unique Rectangle (Type 4) — 4-cell with locked value

BUG Strategies

• BUG Type 1 — Single cell prevents bivalue grid
• BUG Type 2 — Multiple cells share same extra (grid-wide)