Avoidable Rectangle Sudoku: A Careful Uniqueness Technique

Avoidable Rectangle Sudoku starts from a potential deadly pattern

Avoidable Rectangle Sudoku belongs to the family of uniqueness techniques. Look for four cells at the corners of a rectangle made from exactly two rows, two columns, and two 3x3 boxes. A classic deadly rectangle would allow two digits to swap around those four corners while preserving every row, column, and box, producing two solutions. An Avoidable Rectangle differs from a standard Unique Rectangle because one or more of the corners have already been solved during play rather than remaining as candidate cells. If the remaining unsolved corner or corners were allowed to complete the two-digit swap pattern, the puzzle would become ambiguous. In a puzzle guaranteed to have one solution, that completion must be prevented. Avoidable Rectangle Sudoku therefore uses uniqueness as an extra assumption about the puzzle's construction, not merely the visible no-repeat rules.

Check givens before using Avoidable Rectangle Sudoku

The most important safety check in Avoidable Rectangle Sudoku is the status of the solved corners. The uniqueness argument depends on the rectangle being swappable without changing the original givens. If a corner value was supplied as a fixed clue, that clue may already distinguish the two arrangements and the usual avoidable-rectangle logic may not apply. Also confirm that the four corners occupy exactly two boxes. If they span four boxes, swapping the pair may break box constraints, so there is no deadly pattern to avoid. Once the geometry and clue status are correct, compare the two rectangle digits with the candidates in the unsolved corner or corners. Eliminate only the candidate that would complete the ambiguous arrangement. If several extra candidates exist, the exact subtype can resemble a familiar Unique Rectangle case, but the proof should always return to the same question: would this placement create a second valid completion?

Use Avoidable Rectangle Sudoku only on trusted unique puzzles

Avoidable Rectangle Sudoku is not appropriate when the puzzle source does not promise a unique solution. A multiple-solution puzzle can legally contain the pattern that the technique is designed to prevent. On a trusted classic Sudoku, uniqueness methods are widely used, but many solvers still prefer direct constraint logic when it is available because it does not depend on construction assumptions. Shapedoku boards are designed as standard single-solution Sudoku puzzles, so the general uniqueness mindset can apply there as well, even though the symbols are shapes rather than digits. Before reaching for an Avoidable Rectangle, check singles, pairs, locked candidates, and chains. If a direct logical elimination proves the same result, it is usually clearer. When uniqueness is the cleanest route, mark the four corners, identify which are givens and which were solved, and explain the forbidden swap to yourself before removing anything.

If you are unsure whether an Avoidable Rectangle Sudoku pattern is legitimate, perform the swap test explicitly. Imagine the two rectangle digits exchanged at all four corners while leaving every other cell unchanged. Would both rows, both columns, and both boxes still satisfy Sudoku, and would all original givens remain untouched? If yes, you have identified the ambiguity that uniqueness must prevent. If the swap breaks a box or contradicts a given clue, the rectangle is not deadly and the uniqueness elimination is unsupported. This concrete test is more dependable than recognizing a familiar rectangle shape from memory.

• Use four rectangle corners in exactly two rows, two columns, and two boxes.
• Identify the two digits that would create the interchangeable deadly pattern.
• Check whether solved corners were placed during solving rather than fixed as distinguishing givens.
• Eliminate only a candidate that would complete a second valid arrangement.
• Do not use uniqueness logic on a puzzle that may have multiple solutions.
• Prefer a direct row-column-box proof when one is available.