Unique Rectangle Types 2-6
Extreme
Used by Smart Hint
The rest of the Unique Rectangle family: when only two corners are a bare pair, what the other two carry still gives the deadly pattern away.
- Cells that establish the pattern
- Where the conclusion lands
- Candidate ruled out
How it works
- B4 and E4 are a bare {5, 8} pair — the rectangle's "floor". B1 and E1 hold {5, 8} plus extras — the "roof". If the roof ever came down to just {5, 8} too, 5 and 8 could swap around the rectangle and the puzzle would have two solutions.
- This is the Type 4 shape: row 1 has nowhere else to put a 5, so one of B1 and E1 must be the 5.
- That means neither of them can be the 8: an 8 in one roof cell would force the 5 into the other, and the floor pair would then have to take the leftover 5 and 8 — exactly the deadly swap. Eliminate 8 from both roof cells.
- Its siblings work the same way from a different clue: Type 2/5 when both roof cells share one extra digit (that digit lands in one of them, so it dies in any cell seeing both), Type 3 when the roof's extras combine with neighbours into a naked subset, and Type 6 when one pair digit is boxed into the four corners along both rows or both columns.