Sudoku Solver

Expert+

BUG Type 1 (BUG+1)

When only one cell has 3 candidates and all others have 2, the extra candidate must be the solution.

BUG Type 1 (also called BUG+1) is an advanced "uniqueness" strategy that detects when the puzzle is about to enter an impossible state. Unlike logic-based strategies that prove what must be true, BUG uses the fundamental Sudoku rule that every valid puzzle has exactly one unique solution.

This strategy is surprisingly powerful once you understand it—and it can instantly solve a cell that would otherwise require complex chains!

Interactive Example

1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
7
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
4
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
6
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1
1 2 3 4 5 6 7 8 9
9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
4
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
3
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
4
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
1
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
6
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
3
1 2 3 4 5 6 7 8 9
3
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
7
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9

Click "Apply Logic" to see the strategy in action.

Real Example Walkthrough

In the example puzzle above, the solver identifies a BUG+1 state:

The Grid State: - Almost every unsolved cell has exactly 2 candidates - One cell (R8C4) has 3 candidates: {4, 6, 9}

The Analysis:

  1. Count candidate appearances: In R8C4's row, column, and box:
  2. Candidates 4 and 6 each appear exactly 2 times in their respective regions

  3. Candidate 9 appears 3 times in at least one region (this is the "extra")

  4. Apply BUG logic: If R8C4 were 4 or 6, the grid would become a BUG (all cells bivalue, all candidates appearing exactly twice)—meaning two valid solutions!

  5. Eliminate: R8C4 must be 9 to avoid the deadly BUG state. Remove 4 and 6.

Result: R8C4 = 9, instantly solving this cell!

What Is a BUG (Bivalue Universal Grave)?

A BUG (Bivalue Universal Grave) is a grid state where:

  1. Every unsolved cell has exactly 2 candidates
  2. Every candidate appears exactly 2 times in each row, column, and box it belongs to

This creates a deadly pattern—you could swap candidates throughout the grid and both arrangements would be valid. Since a proper Sudoku cannot have two solutions, this state is impossible.

Why "Bivalue Universal Grave"?

Term Meaning
Bivalue Each cell has exactly 2 candidates
Universal This applies to ALL unsolved cells
Grave The puzzle is "dead"—it has no unique solution

BUG Type 1: The "+1" Rule

BUG Type 1 (BUG+1) applies when:

  • All unsolved cells have exactly 2 candidates except one
  • That one cell has exactly 3 candidates
  • One of those 3 candidates is the "extra"—it appears 3 times (not 2) in its row, column, or box

The Logic

The grid is almost a BUG. Only the "+1" cell (with 3 candidates) prevents the deadly pattern.

  • If the +1 cell becomes any of its 2 "normal" candidates, the grid becomes a BUG → impossible
  • Therefore, the +1 cell must be the extra candidate
  • We can eliminate the other candidates from this cell

How to Identify the Extra Candidate

The extra candidate is the one that appears an odd number of times (usually 3) in the cell's row, column, or box, while the others appear exactly twice.

Example from our puzzle:

Candidate Appearances in Row 8 Appearances in Column 4 Extra?
4 2 2 No
6 2 2 No
9 3 2 Yes!

Since 9 appears 3 times in Row 8, it's the extra candidate. R8C4 must be 9.

Step-by-Step: How to Spot BUG+1

  1. Check cell candidate counts: Are almost all unsolved cells bivalue (2 candidates)?
  2. Find the outlier: Is there exactly ONE cell with 3 candidates?
  3. Count appearances: For each candidate in that cell, count how many times it appears in its row, column, and box
  4. Identify the extra: Which candidate appears an odd number of times (not 2)?
  5. Solve the cell: The cell must be the extra candidate; eliminate the others

Visual Recognition

BUG+1 has a distinctive "feel" when you're solving:

  • The puzzle is nearly finished
  • Most remaining cells show only 2 candidates each
  • One cell stubbornly has 3 candidates
  • You can't seem to reduce it with normal techniques

When you see this pattern, check for BUG+1!

Common Misconceptions

"BUG requires ALL cells to be bivalue"

Incorrect. BUG+1 specifically handles the case where ONE cell has 3 candidates. That's the "+1" in the name!

"I need to count all 81 cells"

No. Only check the unsolved cells. Filled cells don't participate in BUG analysis.

"The extra candidate appears 3 times everywhere"

Not necessarily. It only needs to appear an odd number of times in at least one region (row, column, or box). Other regions may have 2.

Why This Strategy Works

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

If a BUG state could exist: - Every bivalue cell could swap its two candidates - The entire grid could be "flipped" to create another valid solution - This violates the single-solution rule

By detecting the "+1" cell that prevents the BUG, we know its extra candidate must be the answer—otherwise, eliminating it would create the impossible BUG state.

Comparison with Related Strategies

Strategy Pattern Cell Count Action
BUG Type 1 Almost BUG + 1 cell with 3 candidates 1 Solve the +1 cell
BUG Type 2 Almost BUG + multiple cells share same extra 2+ Eliminate extra from common peers
BUG Type 3 Almost BUG + extras form naked subset 2+ Eliminate via naked subset
BUG Type 4 Almost BUG + one value locked 2 Eliminate the locked value

BUG vs Unique Rectangle

Feature BUG Unique Rectangle
Scope Entire grid 4 cells only
Cell state All cells bivalue Specific rectangle pattern
Candidate count 2 per cell, 2 per region Same pair in 4 corners
Complexity Easier to spot late-game Can appear mid-game

Tips for Beginners

  1. Look late in the solve: BUG+1 typically appears when few cells remain
  2. Use candidate notation: Mark all candidates—bivalue cells will be obvious
  3. Trust the pattern: If you find a valid BUG+1, the elimination is guaranteed correct
  4. Don't overthink: One cell with 3 candidates + all others with 2 = check for BUG!
  5. Practice counting: The extra candidate count becomes automatic with practice

When BUG+1 Doesn't Apply

  • Multiple cells with 3+ candidates: Try BUG Type 2, Type 3, or Type 4
  • Some cells have 4+ candidates: The grid isn't close enough to BUG state
  • Candidate counts are all even: No extra exists; pattern doesn't apply

Related Strategies

BUG Family

  • BUG Type 2 — Multiple BUG cells share the same extra candidate
  • BUG Type 3 — BUG cells' extras form a Naked Subset
  • BUG Type 4 — One value is locked to BUG cells

Unique Rectangle Family

Unique Loop Family