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BUG+1

Master· L9
Value

Also known as Binary Universal Grave + 1.

BUG means *Binary Universal Grave*: every empty cell has exactly two candidates, and each candidate appears at most twice per house — an invalid state with more than one solution.

BUG+1 is the almost-BUG: every unsolved cell is bi-value except one cell with three candidates. Uniqueness says the extra candidate in that cell must be true.

Why it works

If that extra candidate were false, the grid would become a pure BUG — typically allowing multiple solutions. A unique puzzle refuses that world.

So the extra digit is forced. Place it.

How to spot it

Quick check whenever all-but-one empty cells are bi-value.

Caution. Only for properly unique classic Sudoku. Do not use on variants or multi-solution puzzles.

Demonstration

462793218746567289815693742273841596649752813327872519343427651

A unique classic puzzle cannot fall into a Binary Universal Grave (all bi-value, multi-solution).

462793218746567289815693742273841596649752813327872519343427651

Check whether almost every empty cell has exactly two candidates. Exactly one cell has three — that is BUG+1. The extra digit is 9.

462793218746567289815693742273841596649752813327872519343427651

If 9 were false, the puzzle would fall into that deadly all-bi-value grave with more than one solution.

4627932187465672898156937422738415966497528133927872519343427651

Place 9 in the three-candidate cell. Uniqueness demands it — only on unique classic puzzles.

Example 1

41937283941657182943429561657419718236547384691255263184194275836

Look for an all-bi-value grid with one triple cell.

41937283941657182943429561657419718236547384691255263184194275836

BUG+1 — the extra digit is 8.

419372839416571829434295616574189718236547384691255263184194275836

Place 8. It prevents a non-unique Binary Universal Grave.

Example 2

8654714957123867186457691842538275964542617846183768342751978642

Look for an all-bi-value grid with one triple cell.

8654714957123867186457691842538275964542617846183768342751978642

BUG+1 — the extra digit is 9.

86547149571238671864576918425382759645426178461837683427519798642

Place 9. It prevents a non-unique Binary Universal Grave.

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