Avoidable Rectangle

An Avoidable Rectangle is the inverse of a Unique Rectangle. Instead of analysing candidate cells, it examines solved cells to find patterns that puzzle creators must avoid when designing unique-solution puzzles.

How It Works

The Pattern

Look for four cells forming a rectangle:

• Three cells are already SOLVED (filled during solving, not original clues)
• One cell remains UNSOLVED (has candidates)
• The rectangle spans exactly two boxes

The Deadly Pattern Connection

If the three solved cells form a partial {A, B} / {B, A} swap pattern, the unsolved cell cannot contain the digit that would complete the swap.

       C3       C7
R1   [ 5 ]    [ 8 ]     ← Solved: diagonal pair (5,8)
R5   [ 8 ]    {?}       ← Solved: 8, Unsolved: has 5 as candidate

If the unsolved cell at R5C7 contained 5:

• We'd have: (5, 8) and (8, 5) — a deadly pattern!
• The digits could swap diagonally creating multiple solutions

The Logic

1. Find rectangles with exactly 3 solved + 1 unsolved cells
2. Check if the solved cells form a partial {A, B} / {B, A} pattern
3. The unsolved cell CANNOT contain the digit that completes the deadly pattern
4. Eliminate that candidate

Example

       C3       C7
R1   [ 5 ]    [ 8 ]
       │  ╲   ╱  │
       │    ╳    │
       │  ╱   ╲  │
R5   [ 8 ]    {2,5,6,9}

Analysis:

• R1C3 = 5, R1C7 = 8, R5C3 = 8 (all solved)
• R5C7 = {2, 5, 6, 9} (unsolved)
• Pattern shows: (5, 8) / (8, ?)
• If R5C7 = 5, we'd have (5, 8) / (8, 5) — deadly!
• Eliminate 5 from R5C7

Key Difference from Unique Rectangle

Why "Avoidable"?

The name comes from the puzzle constructor's perspective. When creating a puzzle:

• They must AVOID placing clues that would allow this pattern
• If three cells already form a partial deadly pattern, the fourth cannot complete it
• This is what puzzle creators must check to ensure unique solutions

Finding Avoidable Rectangles

1. Look for solved rectangles — Four cells spanning two boxes, two rows, two columns
2. Count solved vs unsolved — Need exactly 3 solved, 1 unsolved
3. Check the diagonal — Do solved cells form {A, B} / {B, ?} or similar?
4. Find the dangerous candidate — Which digit would complete the deadly swap?
5. Eliminate it — That candidate cannot appear in the unsolved cell

Complexity

Avoidable Rectangle is an advanced technique because:

• Requires tracking which cells are solved vs original clues
• Must verify the rectangular pattern spans exactly two boxes
• Less common than standard Unique Rectangles (needs specific solve state)

Related Techniques

• Unique Rectangle — Works on candidate cells
• BUG — Another uniqueness technique