BUG+1

An almost-all-bivalue grid forces its one tri-value cell.

BUG+1 is an end-game uniqueness trick that turns the promise of a single solution into an immediate placement. A Bivalue Universal Grave is a grid in which every unsolved cell holds exactly two candidates and each digit appears precisely twice in every row, column and box — a shape that is guaranteed to have two solutions. Because a properly set puzzle can have only one, the BUG+1 (bivalue universal grave) sudoku technique hunts for the lone cell still carrying three candidates and forces it to the value that would otherwise complete that deadly, two-solution pattern.

Worked example

A Bivalue Universal Grave "plus one": every unsolved cell is bivalue except R1C1={1,2,3}. In box 1 digit 1 appears three times and 2 and 3 only twice, so R1C1 must be 1 (any other choice gives two solutions).1231213
A Bivalue Universal Grave "plus one": every unsolved cell is bivalue except R1C1={1,2,3}. In box 1 digit 1 appears three times and 2 and 3 only twice, so R1C1 must be 1 (any other choice gives two solutions).

Here every unsolved cell is bivalue except R1C1, which still holds {1,2,3}. Turn to box 1 and count how often each of those candidates appears: digit 1 shows up three times — at R1C1, R1C2 and R2C1 — while 2 and 3 each appear only twice. If R1C1 resolved to 2 or 3, every unit would settle into exactly-twice occurrences and the grid would sink into a Bivalue Universal Grave with two solutions, which a valid puzzle cannot permit. So R1C1 must take the thrice-occurring digit, 1, and it is placed at once.

When to use it

Save BUG+1 for the tail end of a hard solve, when nearly every remaining cell has been whittled down to two candidates. Scan for exactly one cell that still shows three candidates — that is your +1 cell. Then look through that cell's row, column and box for the candidate appearing three times rather than twice; that digit is the answer, just as 1 was for R1C1.

How to use it

  1. Spot the bivalue grid. Notice that every unsolved cell has exactly two candidates, except one cell that has three.
  2. Avoid the deadly pattern. A fully bivalue grid (a BUG) would have two solutions — which a real puzzle never has.
  3. Place the odd digit. In the tri-value cell, place the candidate that appears three times in its box (an odd number).
Practice on a real puzzle

Frequently asked questions

What is a BUG+1 in Sudoku?

BUG+1 is a uniqueness technique used at the very end of a solve. A Bivalue Universal Grave (BUG) is a grid state where every unsolved cell has just two candidates and each candidate appears exactly twice in every row, column and box — a pattern that always yields two solutions. When the grid is a single candidate away from that state, the one cell carrying a third candidate must take the value that breaks the pattern. In the worked example, R1C1 holding {1,2,3} resolves to 1.

How do I spot the +1 cell?

The +1 cell is simply the only cell still left with three candidates instead of two — every other unsolved cell has already reduced to a bivalue pair. Once you have found it, count each of its three candidates across its row, column and box: the one appearing three times rather than twice is the solution. For R1C1 that digit was 1, which appeared three times in box 1 at R1C1, R1C2 and R2C1.

Does BUG+1 rely on the puzzle having a unique solution?

Yes. BUG+1 assumes the puzzle has exactly one solution — the whole argument is that a Bivalue Universal Grave would produce two valid solutions, which a properly set puzzle forbids. On a grid that genuinely has multiple solutions that logic collapses and the deduction becomes unsafe. Only apply it to puzzles you know are well-formed with a single answer.