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BUG (Bivalue Universal Gravekard)

A uniqueness shortcut: when every unsolved cell is bi-value except one, the odd candidate is the answer.

BUG — Bivalue Universal Grave — is a late-game uniqueness pattern. If the grid reaches a state where every remaining cell has exactly two candidates except a single cell with three, then placing the "extra" candidate is the only way to keep the solution unique.

A full BUG (all cells bi-value) would mean two solutions, which a valid puzzle cannot have — so the technique breaks that symmetry just before it forms.

How to spot it

Once almost every empty cell is bi-value, look for the lone tri-value cell. The digit that appears an odd number of times in that cell’s row, column, or box is the one to place — it is the candidate whose removal would create the deadly bi-value grave.

  • Nearly all empty cells are bi-value.
  • Exactly one cell has three candidates.
  • Place the candidate that appears an odd number of times in a unit.
All pairs except one cell — the tri-value cell takes the thrice-seen digit.

Worked example

  1. Late in an expert grid every empty cell shows two candidates — except one showing {2,5,7}.
  2. Counting 2s, 5s and 7s in its column, the 7 appears three times (odd), the others twice.
  3. A bi-value grave would have two solutions.
  4. To keep uniqueness, the tri-value cell must be 7.
  5. Place 7 and finish with singles.

Try it yourself

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

Tap a cell, then a number, to practise.

Frequently asked questions

When does BUG apply?
Only very late, when the candidate grid has collapsed almost entirely to bi-value cells.
Is BUG a uniqueness technique?
Yes — like unique rectangles, it assumes the puzzle has exactly one solution.

Related techniques

Practice: BUG (Bivalue Universal Gravekard)

Put the BUG (Bivalue Universal Gravekard) to work on a live board — free puzzles with notes, hints and four difficulty levels.

Try it on a live board

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