Unique Rectangle

The Unique Rectangle (UR) is the most common of the "uniqueness" techniques — the ones that use a fact no other technique does: a proper Sudoku has exactly one solution. If a pattern would create a second solution, it can't be allowed, and that alone is enough to make an elimination.

The deadly pattern

Imagine four cells at the corners of a rectangle, spread across exactly two rows, two columns and two boxes, and every one of them holding the same two candidates — say {2, 6}. If the puzzle were ever filled so all four contained only 2 and 6, you could swap them (2↔6) and get a second valid grid. A proper puzzle can't allow that, so this "deadly pattern" is forbidden.

That gives you a lever. If three of the four corners are exactly {2, 6} and the fourth has an extra candidate — say {2, 6, 9} — then the fourth cell cannot be 2 or 6 (that would complete the deadly pattern). It must be the 9. Delete the 2 and the 6 from it.

Three corners are {2, 6}; the fourth is {2, 6, 9}. Filling all four with just 2 and 6 would give two solutions, so the fourth cell must be the 9.

Step by step

Look for three cells with the same two candidates that form three corners of a rectangle.
Check the fourth corner. It must share those two candidates plus at least one more.
Confirm two boxes. The four corners must span exactly two boxes — otherwise the uniqueness argument doesn't hold.
Eliminate the two shared candidates from the fourth corner (this is the Type 1 Unique Rectangle).
Re-scan. The fourth cell is often left as a single.

A word of caution

Uniqueness techniques only work on puzzles that are guaranteed to have a single solution — which every SudokuStreak puzzle is. On a hand-made puzzle of unknown quality the argument can mislead, so purists sometimes avoid them. There are also more advanced UR types (2 through 6) for when the extra candidates are arranged differently, but Type 1 above is by far the most common.

Common mistakes

Only one box. If the four corners sit in a single box row and box column pair that spans just one box, there's no deadly pattern. Two boxes are essential.
The fourth cell has no extra. If all four are exactly {2, 6}, the puzzle is already broken — the UR needs one corner with an extra candidate.
Eliminating from the wrong corner. The extras stay; the two shared digits go, and only from the corner that has the extra.

Which Sudoku types is this best for?

The same logic applies across variants, but it pays off more in some than others.

Great fit Classic Sudoku The uniqueness argument holds on any proper single-solution Classic grid. → Works Killer Sudoku Applies, but Killer's cage constraints usually settle things another way first. → Works Sudoku X Valid, though the diagonals change which rectangles are truly deadly. → Works Samurai Sudoku Each sub-grid is a proper puzzle, so the technique applies within each one. →