BUG

Bivalue Universal Grave

By Minimal Sudoku Team•Last updated: January 28, 2025

BUG (Bivalue Universal Grave) is a uniqueness technique that triggers when almost every unsolved cell has exactly 2 candidates. This "deadly" pattern would allow multiple solutions — so the cell preventing it must resolve a specific way.

⚡Quick Summary

Pattern: All unsolved cells have exactly 2 candidates, except one with 3
Problem: If all cells were bi-value, multiple solutions would exist
Solution: The cell with 3 candidates must be set to the "extra" candidate
Difficulty: Expert — rare but powerful when it appears

The Concept

A "Bivalue Universal Grave" is a grid state where:

Every unsolved cell has exactly 2 candidates
Each candidate appears exactly twice in each unsolved row, column, and box

This state would allow swapping candidates along chains, creating multiple solutions. Since valid puzzles have unique solutions, a true BUG state is impossible.

The Deadly State

🐛 The BUG State

If all unsolved cells had exactly 2 candidates each, with each candidate appearing exactly twice per unit, the puzzle would have multiple solutions — a "grave" for uniqueness.

Deadly BUG state (must be avoided):

All remaining cells are bi-value:
[1,2] [1,2] [3,4] [3,4] ...

Each candidate appears exactly twice per row/column/box.
→ Candidates could swap along chains
→ Multiple valid solutions!

The Golden Rule

✓ BUG+1 Rule

If the grid is one step away from a BUG state — all unsolved cells are bi-value except one cell with 3 candidates — that cell must be set to its unique "extra" candidate (the one that would break the BUG).

The "extra" candidate is the one that appears 3 times in some unit (instead of 2). Setting the cell to this value prevents the BUG state.

How to Spot a BUG

Check unsolved cells

Count the candidates in each unsolved cell. Most should have exactly 2.

Find the exception

Look for exactly one cell with 3 candidates. All others must have 2.

Identify the extra candidate

In the cell with 3 candidates, find which candidate appears 3 times in its row, column, or box.

Place the digit

Set the cell to the extra candidate — this breaks the BUG.

Example

Grid state:
All unsolved cells have 2 candidates, except R5C5 with [2,4,7].

Checking R5C5:
• Candidate 2: appears 2× in row 5 ✓
• Candidate 4: appears 2× in row 5 ✓  
• Candidate 7: appears 3× in row 5 ← EXTRA!

Without the 7 in R5C5, we'd have a BUG state.
→ Therefore R5C5 = 7

Instant Placement

BUG always gives you a direct placement — no eliminations, just solve the cell!

Detection Tips

Late-Game Technique

BUG typically appears when a puzzle is nearly solved. If you have 10-20 cells left and they're almost all bi-value, check for BUG.

Quick Count

Scan unsolved cells — if they're all showing 2 candidates except one showing 3, investigate immediately.

Assumes Unique Solution

Like all uniqueness techniques, BUG assumes the puzzle has exactly one solution. It won't work on puzzles with multiple solutions.

Uniqueness Techniques

🔲Unique Rectangle ⬜Rectangle Elimination

Advanced

Unique Rectangle

Another uniqueness technique based on avoiding deadly patterns.

BUG