Proven Sudoku
Extended Unique Rectangle
Also called EUR, Extended UR, Six-cell unique rectangle.
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
A bigger version using six squares and three numbers instead of four and two. If those six held only those three numbers, they could be shuffled for a second answer. So something has to break it.
The exact rule, for stronger players
The rule, stated exactly: Six cells spanning two boxes and three lines, holding three digits in a pattern that would permute freely. Extra candidates in one cell are forced, or the pattern digits are eliminated from it.
What it removes: Remove the pattern digits from the cell carrying extras, or place the extra where only one exists.
Why it works: The same permutation argument as the four-cell rectangle, extended to a three-digit, six-cell configuration that admits two completions. This technique is only valid when the puzzle is known to have exactly one solution. It is not a deduction about Sudoku rules, it is a deduction about the puzzle setter's promise. On a grid with multiple solutions it produces wrong answers.
Worked examples
None yet. This pattern does not turn up in our daily boards, so there is no real example to show. We would rather wait than draw a fake one.
Learn these first
- Unique RectangleFour squares in a rectangle across two boxes, all holding the same two numbers.
- Naked TripleThree squares in one group share the same three digits between them.
Related uniqueness
- Hidden Unique RectangleThe rectangle trick again, but the giveaway is hidden.
- Reverse BUGThis one uses the numbers you have already filled in, not the ones still open.
- Unique LoopLike a rectangle but longer, a ring of squares all sharing two numbers.
- Unique Rectangle Type 1Three corners of the rectangle hold only the two numbers.
- Unique Rectangle Type 2Two corners hold only the pair.
How often does it come up?
Our rough estimate: uncommon. ADDED BEYOND APPENDIX A, found in research.