Tridagon

Tridagon (also known as "Thor's Hammer") is an advanced uniqueness technique that detects patterns where three digits appear across four boxes in a rectangular arrangement. When these cells would create a cyclical parity violation, special "Guardian" candidates can be eliminated.

Understanding the Pattern

The Four-Box Rectangle

Tridagon requires four boxes arranged in a 2×2 pattern:

     Stack 1    Stack 2
     ┌─────┐    ┌─────┐
Band │Box 0│    │Box 1│
  1  │     │    │     │
     └─────┘    └─────┘
     ┌─────┐    ┌─────┐
Band │Box 3│    │Box 4│
  2  │     │    │     │
     └─────┘    └─────┘

The Triple Pattern

In each of the four boxes:

• Three cells contain the same candidate triple {A, B, C}
• Total: 12 cells across 4 boxes

Parity Types

Each box has a parity based on how its three cells are arranged:

Rising Parity: Cells create one diagonal pattern Falling Parity: Cells create the opposite diagonal pattern

The Deadly Configuration

If three boxes have one parity and one box has the opposite (3:1 ratio), a cyclical violation occurs — the puzzle would have no solution without intervention.

Guardian Cells

A Guardian cell is one that contains the triple {A, B, C} PLUS extra candidates.

These extra candidates prevent the deadly pattern from forming.

The Elimination Rule

If exactly ONE Guardian cell exists:

• The triple digits {A, B, C} can be eliminated from it
• The Guardian MUST be one of its extra candidates
• This breaks the deadly pattern

Multiple Guardians

If multiple Guardian cells exist:

• They may form pointing pairs
• Additional eliminations may be possible
• More complex analysis required

Visual Example

Box 0:              Box 1:
{A,B,C} .  .       .  {A,B,C}  .
.  {A,B,C} .       .  .  {A,B,C}
.  .  {A,B,C,X}    {A,B,C} .  .
      ↑
   Guardian (has extra X)

Box 3:              Box 4:
.  {A,B,C}  .      {A,B,C}  .  .
{A,B,C}  .  .      .  .  {A,B,C}
.  .  {A,B,C}      .  {A,B,C}  .

If the parity creates a 3:1 violation, and Box 0 has the only Guardian cell:

• Eliminate A, B, C from that Guardian cell
• It must be X

The Parity Logic

Why does parity matter?

In a valid Sudoku:

• Each digit appears once per row, column, and box
• The three cells with {A, B, C} in each box must eventually hold A, B, and C
• The arrangement across four boxes creates constraints
• A 3:1 parity split makes it impossible to consistently place all digits

Guardian cells with extra candidates are the "escape valve" — they allow the pattern to resolve without contradiction.

Complexity

Tridagon is an expert-level uniqueness technique:

• Complex geometry: Four boxes in rectangular arrangement
• Parity analysis: Must calculate and compare box parities
• Rare occurrence: Few puzzles require this technique
• Guardian logic: Extra layer of analysis on top of pattern

Relationship to Other Uniqueness Techniques

Tridagon is the largest standard uniqueness pattern.

Tips

1. Look for the rectangle — Four boxes in 2×2 arrangement
2. Find triple cells — Three cells per box with same {A, B, C}
3. Check parity — Is there a 3:1 split?
4. Find Guardians — Cells with extras are elimination targets
5. Trust the app — Complex pattern, best found automatically

More Puzzles

• Tridagon ex. 1

Related Techniques

• Unique Rectangle — Simpler deadly pattern
• Extended Unique Rectangle — Six-cell version
• BUG — Another uniqueness technique