Unique Rectangle practice sheets
Three corners of a rectangle hold the same pair. If the fourth did too, the puzzle would have two solutions — so it must be something else.
The only technique that argues from the answer key
Every other technique on this site reasons from the rules: this digit is already here, so it cannot be there. Unique Rectangle reasons from something else — the promise that the puzzle has exactly one solution.
Take four cells at the corners of a rectangle spanning two rows and two columns, sitting in exactly two boxes. Suppose three of them hold only {2, 3}. If the fourth also held only {2, 3}, the four cells could be filled 2-3-2-3 or 3-2-3-2, and both would satisfy every row, column and box. Two solutions. So a well-formed puzzle cannot allow it: the fourth corner must be something other than 2 or 3.
That is Type 1, and it is the version on these sheets. The elimination is the two digits of the shared pair, removed from the fourth corner. Nothing gets placed.
Because the argument leans on uniqueness, it is the one technique where a broken puzzle gives a wrong answer rather than a dead end. Every puzzle here is checked for a single solution before it ships.
Why a dedicated sheet
In the wild you meet a Unique Rectangle roughly once a puzzle, at the moment when everything else has stalled — and it is easy to talk yourself out of, because the conclusion feels like cheating. Everyone who learns it has the same first reaction: that cannot be a valid deduction.
Drilling it is the fix. When you have found twenty of them, the shape recognition becomes instant and the doubt goes away.
Every puzzle is generated and then replayed with the cheapest technique first; it is kept only if a Unique Rectangle appears on that path. The filter runs in your browser, so the set is new on every visit.
What the grader guarantees
Every puzzle needs at least one Unique Rectangle. Nothing on the sheet asks for a technique more than one tier above it, so the hardest extra step you can meet is a W-Wing, a Jellyfish or a chain. That is the difficulty ladder doing its job, not a mistake in the filter.
What the filter cannot guarantee is that the rectangle is pretty. Some boards hide it behind a lot of pencil marks. That is what practice is for.
Making the search mechanical
- Complete the candidate marks. This technique lives entirely inside two-candidate cells. Half-marked boards hide it completely.
- Pair up rows and columns. For each pair of rows, look at the columns where both rows have an empty cell. A rectangle needs two such columns.
- Check the box count. The four corners must sit in exactly two boxes. If they spread across four boxes, there is no uniqueness risk and no deduction.
- Look for three matching pairs. Three corners with the identical
{2, 3}is the shape. The fourth corner is your target. - Confirm the fourth carries extras. It must contain both digits of the pair and something else. If it contains only the pair, the puzzle is broken — you have found a second solution, not a technique.
Printing it
Scale 100%, A4 or Letter. Candidate marks on is mandatory here — the pattern is entirely invisible on a bare grid, more so than for any other technique. One puzzle per page to learn on, four per page to drill.
Related practice
The full guide to Unique Rectangle walks a real position and explains why the uniqueness argument is sound rather than a shortcut. X-Wing is the pattern that looks most similar and is completely unrelated — same rectangle, entirely different reasoning.