The four hyper regions

The four hyper regions are the structural addition that turns a classic Sudoku into a Hyper Sudoku (or Windoku). They're 3×3 blocks, each obeying the same uniqueness rule as a row, a column, or a standard box. This article walks through where they sit, why they sit there, and how to develop the habit of seeing them while solving.

Where they sit

The four hyper regions occupy four specific 3×3 blocks inside the grid. If you number the rows and columns 1 through 9 (top-to-bottom, left-to-right), the four regions are:

The top-left hyper region covers rows 2–4, columns 2–4. The top-right hyper region covers rows 2–4, columns 6–8. The bottom-left hyper region covers rows 6–8, columns 2–4. The bottom-right hyper region covers rows 6–8, columns 6–8.

Each region sits inside one of the four quadrants of the board, offset by one cell from the corner on each side. The four regions are equally spaced, equally sized, and don't touch each other. Between any two adjacent regions, there's exactly one column or row of cells that doesn't belong to any hyper region — call this the gap. The gap forms a + shape running through the middle of the grid.

How many cells participate

Nine cells per region, four regions, no overlap — so 36 cells in total belong to a hyper region. The other 45 cells (the four corners and the + shaped gap in the middle) play exactly as in classic Sudoku, with three units each. The 36 hyper-region cells play with four units each.

A useful mental picture: about 44 percent of the grid carries the extra constraint, and the rest is classic.

Why those positions

The positions are chosen so that the extra constraint sits where a classic Sudoku is least constrained naturally. Classic Sudoku's boxes are 3×3 corners of the grid; the hyper regions are 3×3 blocks offset from those corners. The result is that every hyper region overlaps four different standard boxes — never just one — so a placement inside it constrains digits across a wider area of the board than the same placement in a standard box would.

This is the design choice that gives the variant its character. If the hyper regions were positioned on top of the standard boxes — say, the centre 3×3 of each row of boxes — they wouldn't add useful constraint, because their cells would already share a unit with each other through the box rule. Offsetting them by one cell in each direction means every hyper-region cell shares its hyper region with eight cells that are spread across four different boxes. The constraint covers ground a standard box can't.

How to see them while solving

The hyper regions are visually marked on Sudoku Mountain's board with a soft coral outline. You don't have to remember their positions cold; the geometry is visible at all times. For the first few puzzles, this is enough — your eye learns to include the hyper regions in the unit scan when working on a cell that sits inside one.

After three or four puzzles, the four regions become familiar enough that you can pick them out at a glance even without the outline. Many regular Hyper Sudoku solvers report being able to draw the four regions blind after about ten puzzles.

The visual cue isn't a crutch; it's just a faster way to learn the geometry. Plenty of puzzle books print Hyper Sudoku grids with the hyper regions shown only as faint background tinting, and good solvers adapt to either presentation within a puzzle or two.

The most useful cells to focus on

There are four cells that participate in the densest cluster of units anywhere on the board: the cells at (2, 2), (2, 8), (8, 2), and (8, 8). Each of these sits at the corner of a hyper region, the corner of a standard box, and at a row and column position with no other hyper-region overlap. Watch those cells — they're often where the variant-specific deductions surface.

The four cells at the centre of each hyper region — (3, 3), (3, 7), (7, 3), (7, 7) — also reward attention. They sit dead-centre in their hyper region and benefit fully from any deduction that narrows the region's candidates.

If you'd like a structured introduction to the practical tactics built on these positions, when hyper regions narrow it down walks through the patterns most worth recognising. Or try a hard Hyper Sudoku directly — at that tier, the regions stop being decoration and start carrying significant deductive weight.