Cross-region deduction
A Hyper Sudoku move using the overlap between a hyper region and a standard 3×3 box: locking a digit to a shared sub-region eliminates it from the rest of both units.
Cross-region deduction is the family of Hyper Sudoku moves that exploit the geometric overlap between a hyper region and a standard 3×3 box. The two units share cells — a hyper region overlaps exactly four standard boxes, contributing a 2×2 or 2×1 sub-block to each — and a digit that's locked to one of those shared sub-blocks gets eliminated from both units at once.
How it works
Consider the top-left hyper region (rows 2–4, columns 2–4). Its cells span four standard boxes: the top-left box (rows 1–3, columns 1–3) contributes the four cells (2, 2), (2, 3), (3, 2), (3, 3); the top-middle box (rows 1–3, columns 4–6) contributes (2, 4) and (3, 4); the middle-left box (rows 4–6, columns 1–3) contributes (4, 2) and (4, 3); and the middle-centre box (rows 4–6, columns 4–6) contributes (4, 4).
Suppose, after row and column reductions, the digit 5 in the top-left hyper region is locked to its two cells in the top-left standard box — (2, 2) and (3, 3), say. The hyper region uniqueness rule says 5 appears exactly once in the region, and the only candidates are inside the top-left standard box. The 5 must therefore appear in one of those two cells.
That, by itself, eliminates 5 as a candidate from the other cells of the top-left standard box: (1, 1), (1, 2), (1, 3), (2, 1), (3, 1), (3, 2), and (2, 3). The deduction works just like locked candidates (pointing) — except the locking unit is a hyper region rather than a standard box.
When it fires
Cross-region deductions appear at the medium tier and above. They're particularly common at hard and expert, where the variant's construction often deliberately produces overlap-locked candidates as a key load-bearing move.
The deduction has the same shape as classic locked candidates — pointing or claiming, depending on which unit is the locking one and which is the eliminating one. The novelty is just that one of the two units involved is a hyper region.
For the practical scan habit and the wider list of hyper-region-aware moves, see when hyper regions narrow it down.
See also
- Hyper Sudoku— A Sudoku variant with four extra 3×3 regions overlaid on the standard grid, each obeying the uniqueness rule. Also called Windoku in continental European communities.
- Hyper region— One of the four extra 3×3 regions in a Hyper Sudoku (Windoku). Each region carries the same digit-uniqueness rule as a row, column, or standard 3×3 box.
- Hyper pair— A naked pair where both cells lie in the same hyper region of a Hyper Sudoku (Windoku). Eliminates the two pair digits from every other cell of that region.
- Hyper-only cell— A Hyper Sudoku (Windoku) deduction: a cell where row, column, and standard box together leave multiple candidates, and the hyper region alone forces the digit.
- Pointing pair (locked candidates)— When a digit's only possible cells inside a 3×3 box all share a row or a column, that digit can be eliminated from the rest of that row or column outside the box.
- Box-line reduction (locked candidates)— When a digit's only possible cells inside a row or column all sit in the same 3×3 box, that digit can be eliminated from the rest of that box.
Read more
- When hyper regions narrow it down
A practical tactic for Hyper Sudoku and Windoku: scan the hyper region as a fourth unit when row, column, and box reasoning runs out. Worked patterns and where they fire.
- The four hyper regions
Where the four extra 3×3 regions sit inside a Hyper Sudoku (Windoku) board, why they're positioned that way, and how to spot them while solving.