GridWits
Extreme tier Technique 38 of 46 Used by Smart Hint

Unique Rectangle

Uses the fact that a proper Sudoku has exactly one solution to rule out candidate patterns that would create a second, deadly duplicate.

How it works

  1. 1B1, E1 and B2 all hold exactly the same two candidates, {2, 5} — three corners of a rectangle across two rows, two columns and exactly two boxes.
  2. 2Two boxes is the part that matters: only then can 2 and 5 swap all the way round the rectangle without any row, column or box noticing. Spread over four boxes there is nothing to deduce.
  3. 3If E2 were also just {2, 5}, that swap would give the puzzle two solutions, which a real Sudoku never has — so strike both and leave the 9.

Play a Sudoku that needs this technique →

A 1 B 2 C 3 D 4 E 5 F 6 G 7 H 8 I 9 2 5 2 5 2 5 2 5 9 2 5 2 5 2 5 2 5
  • Cells that establish the pattern
  • Where the conclusion lands
  • Candidate ruled out
Next in the ladder BUG (Bivalue Universal Grave) →

Assuming a unique solution: if every empty cell is bivalue except one trivalue cell, and every candidate has the required even house counts except one extra digit, that cell must hold the extra digit.