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81 Unique Pairs: The Core Rule of Color Sudoku

Suirodoku is a color sudoku variant where each cell combines a number (1-9) and a color (9 colors). This creates 81 unique number-color pairs — and that's what makes solving fundamentally different from classic sudoku.

81 unique pairs in Suirodoku - visual representation of number-color combinations

The Simple Math

9 × 9 = 81

9 numbers × 9 colors = 81 unique combinations.

Each number-color pair exists exactly once in a completed Suirodoku grid. There is only one "Red 5", only one "Blue 3", only one "Green 7"...

Like a deck of cards: Just as a deck has 52 unique cards (13 ranks × 4 suits), Suirodoku has 81 unique cells (9 numbers × 9 colors).

What This Means

In classic Sudoku, the number 5 appears 9 times in the grid (once per row).

In Suirodoku, the number 5 also appears 9 times — but each one has a different color:

  • Red 5, Blue 5, Green 5, Yellow 5...
  • Each is unique and appears only once
  • No two cells are identical
81 unique number-color pairs displayed as colored cubes

Key Points

81
cells in the grid
81
unique combinations
0
duplicates

Sudoku vs Suirodoku

Aspect Sudoku Suirodoku
Cell content Number only Number + Color
Unique elements 9 (numbers 1-9) 81 (all pairs)
Duplicates Each number appears 9× No duplicates

Why It Matters

The 81 unique pairs enable two exclusive techniques:

These techniques only work because each pair is unique. If "Red 5" existed twice, you couldn't deduce anything from tracking it!

How to Use 81 Unique Pairs While Solving

  1. Identify the pair you need: When you place a number, ask "which color?" — or when you place a color, ask "which number?"
  2. Scan for eliminations: If 7-Blue exists somewhere, no other cell can be 7-Blue. Use this to narrow down possibilities.
  3. Apply Rainbow/Chromatic: Track all 9 instances of a number (Rainbow) or a color (Chromatic Circle) to find the missing one.