Sudoku-Y

Advanced

BUG+1: one triple-candidate cell is not enough

Do not choose the odd-looking candidate just because only one cell has three possibilities.

The condition covers the whole board

For the BUG structure discussed here, every unsolved cell is bivalue and every candidate digit present in a unit occurs exactly twice there, across rows, columns and boxes. Such a structure does not have a unique solution. BUG+1 has one extra candidate in one cell whose removal would leave an actual BUG.

HoDoKu — Uniqueness · SudokuWiki — BUG

Our conditional example

Suppose E5={2,6,9} is the only trivalue cell. Assume a complete check establishes that removing its 6 makes every unsolved cell bivalue and every remaining candidate occur twice in each relevant unit. In a uniquely solvable Classic puzzle with sound candidates, the extra candidate must be true: E5=6.

No 81-cell grid is supplied here to establish that global check. This example teaches the conditional argument; seeing {2,6,9} alone does not satisfy it.

One row count is insufficient

Even if 6 occurs three times in row E, inspect column 5, the middle box and all other units too. If removing it leaves some remaining digit only once in a unit, the result is not the stated BUG structure. Picking the most frequent digit is not a proof.

Know when to skip it

Use complete candidates and established uniqueness. If notes might be missing, repair that uncertainty first. Being near the end of a puzzle does not replace a missing premise; singles or chain reasoning may offer another route.

In Classic 9×9, use Scan to scan the current entries, inspect justified eliminations and open this lesson. Chain and ALS searches are bounded; UR Type 1 and BUG+1 require verified uniqueness. Reading this lesson never changes your saved game.

Try before looking

Try before revealing

There is one trivalue cell, but removing the suspected extra leaves only one candidate 9 in a column. Has the BUG check passed?

Show explanation

No. Every remaining candidate must meet the two-occurrences condition in every relevant unit, not merely in the exceptional cell.

References and further reading

Read the source explanations and compare them with our examples. Links are references, not endorsements or claims of affiliation.