Hyper Sudoku: The Windows, the Rules, and the Hidden Fifth Region

Hyper sudoku is a standard 9x9 sudoku with four extra shaded 3x3 regions laid over the grid, each of which must also contain the digits 1 through 9 exactly once. Everything else is unchanged — rows, columns, and the nine normal boxes all work as usual. The four shaded blocks simply add a fourth constraint on the 36 cells they cover.

That's the version you'll read everywhere. What almost nobody mentions is that those four windows silently create five more complete regions that the puzzle never draws, and finding them turns a fiddly variant into a fast one. That derivation is the centerpiece of this guide, and it's a genuine consequence of the rules rather than a heuristic.

The rules of hyper sudoku

Fill the grid so that every row, every column, every 3x3 box, and every one of the four shaded windows contains the digits 1 through 9 once each.

Four constraints stacked:

1. Rows. Each of the 9 horizontal lines holds 1–9, once each.
2. Columns. Each of the 9 vertical lines holds 1–9, once each.
3. Boxes. Each of the 9 bold 3x3 blocks holds 1–9, once each.
4. Windows. Each of the 4 shaded 3x3 regions holds 1–9, once each.

The windows overlap the boxes — they are not an alternative to them. A cell inside a window belongs to a row, a column, a box, and a window, so it has four units watching it instead of three. Nothing is added, nothing is ordered, and the diagonals still mean nothing unless a puzzle explicitly says otherwise. The classic foundations are on our sudoku rules page and all of them still apply.

Where the four windows sit

The windows occupy rows 2–4 and rows 6–8, crossed with columns 2–4 and columns 6–8. Their position is fixed by convention and is the same in every published puzzle of this type.

Written out, using RxCy for row x column y:

The effect is a border of unshaded cells one square wide around the outside of the grid, plus an unshaded cross running along row 5 and column 5. Thirty-six cells are inside windows; forty-five are not.

Crucially, each window straddles four different boxes. Take the top-left window, spanning R2–R4 and C2–C4. It overlaps box 1 (R1–R3, C1–C3) in four cells, box 2 (R1–R3, C4–C6) in two cells, box 4 (R4–R6, C1–C3) in two cells, and box 5 (R4–R6, C4–C6) in one cell. Four plus two plus two plus one is nine. That straddling is where all the interesting deductions come from.

The five hidden regions

The four drawn windows force five more nine-cell groups that also contain 1 through 9 exactly once — and the puzzle never marks them. This is the most useful thing you can know about the variant, and it follows directly from the rules.

Here's the argument for the first one. Look at rows 2, 3, and 4 together: 27 cells, containing each digit exactly three times. Two full windows sit inside those rows — the top-left one and the top-right one — and each contains all nine digits once. That accounts for 18 cells and two full sets of digits. The remaining 9 cells in rows 2–4 are the ones in columns 1, 5, and 9, and they must therefore hold the third set: 1 through 9, once each.

Run the same argument three more times and you get:

Region E is the prettiest of the five. Columns 1, 5, and 9 hold 27 cells and three of each digit. Regions A and B account for 18 of those cells and two full sets. The nine cells left over sit at the intersections of rows 1, 5, 9 with columns 1, 5, 9 — the four corners, the four edge midpoints, and the dead center of the grid — and they hold 1 through 9 once each.

Add it up: four windows plus five derived regions is nine groups of nine cells, and 4 × 9 + 5 × 9 = 81. The nine regions tile the entire board exactly once. The variant hands you a complete second partition of the grid for free, and most solvers never use it.

A verified hyper sudoku grid

Here is a complete, valid solution with all four windows satisfied. Shaded window cells are the ones in rows 2–4 and 6–8 crossed with columns 2–4 and 6–8.

`` 4 8 3 | 9 5 7 | 2 6 1 9 1 5 | 3 6 2 | 7 4 8 2 6 7 | 8 4 1 | 9 5 3 ------+-------+------ 1 9 4 | 2 7 3 | 6 8 5 6 5 2 | 4 9 8 | 3 1 7 7 3 8 | 6 1 5 | 4 2 9 ------+-------+------ 3 2 9 | 5 8 6 | 1 7 4 5 4 1 | 7 2 9 | 8 3 6 8 7 6 | 1 3 4 | 5 9 2 ``

Check the windows:

• Top-left (R2–R4, C2–C4): 1, 5, 3 / 6, 7, 8 / 9, 4, 2 — all nine.
• Top-right (R2–R4, C6–C8): 2, 7, 4 / 1, 9, 5 / 3, 6, 8 — all nine.
• Bottom-left (R6–R8, C2–C4): 3, 8, 6 / 2, 9, 5 / 4, 1, 7 — all nine.
• Bottom-right (R6–R8, C6–C8): 5, 4, 2 / 6, 1, 7 / 9, 8, 3 — all nine.

Now check hidden region E — rows 1, 5, 9 crossed with columns 1, 5, 9. Those cells hold 4, 5, 1 from row 1; 6, 9, 7 from row 5; and 8, 3, 2 from row 9. That's 1 through 9, once each, exactly as the derivation promised. Hidden region A (rows 2–4, columns 1, 5, 9) gives 9, 6, 8 / 2, 4, 3 / 1, 7, 5 — complete too.

How to solve a hyper sudoku

Solve the windows first, then use window-box interactions, then fall back on ordinary technique. The extra constraint is front-loaded: it does its best work in the opening, which is why these puzzles start faster and finish slower than they look.

Start by crosshatching the windows

Treat each window as a tenth, eleventh, twelfth, and thirteenth box. Pick a digit and ask where it can go in each window, exactly as you would for a normal box. Because a window's nine cells are spread across three rows, three columns, and four boxes, a single placement elsewhere on the grid often knocks out three or four window cells at once.

This is why these puzzles carry fewer givens than a classic sudoku — often in the low twenties where a standard puzzle at similar difficulty would want twenty-five or more. Four extra units of constraint replace several clues.

Use window-box interaction

When a digit inside a window is confined to the cells that window shares with one box, eliminate it from the rest of that box. This is ordinary locked-candidate logic applied across the overlap, and it's the highest-yield technique the variant offers.

A worked example. Consider the top-left window (R2–R4, C2–C4) and the digit 7. Suppose you already know two things:

• Row 4 contains a 7 somewhere outside the window — say at R4C7. That rules out 7 at R4C2, R4C3, and R4C4.
• Column 4 contains a 7 somewhere outside the window — say at R7C4. That rules out 7 at R2C4 and R3C4.

Five of the window's nine cells are gone. The survivors are R2C2, R2C3, R3C2, and R3C3 — and all four sit inside box 1. So the 7 for box 1 is somewhere in that 2x2 block, which means 7 can be eliminated from R1C1, R1C2, R1C3, R2C1, and R3C1 — the five cells of box 1 that fall outside the window. Five eliminations from a digit you never actually placed.

The reverse direction works just as well: if a digit in a box can only sit inside the window, it's eliminated from that window's other six cells.

Then use the hidden regions

When window and box logic runs dry, check regions A through E before you start hunting for X-Wings. Hidden region E in particular is easy to scan — nine cells at memorable positions — and because it draws from three separate bands and three separate stacks, it frequently resolves a cell that no ordinary unit can touch.

Solvers who skip the hidden regions end up reaching for chains and fish on puzzles that don't need them. If a windoku feels harder than its rating, this is almost always the reason.

Everything else still applies

Naked singles, hidden singles, pointing pairs, box-line reduction, naked and hidden subsets, X-Wing, and XY-Wing all work unchanged. The variant adds units; it doesn't remove any technique. Our guide to XY-Wing sudoku transfers with no adjustment beyond remembering that two cells can now "see" each other through a window as well as through a row, column, or box.

That last point is the one to internalize. Two cells in the same window are peers even if they share no row, no column, and no box. R2C2 and R4C4 are peers here and are not peers in a classic grid.

The names this variant goes by

Hyper sudoku, windoku, NRC sudoku, and four-square sudoku all describe the same puzzle. If a grid has four shaded 3x3 blocks in the positions above, the name on the page doesn't matter.

Be careful with one near-neighbor: Sudoku X adds the two long diagonals as extra units, not four blocks. Some publishers combine the two, producing a grid with windows and diagonals. Read the instructions rather than the title.

Related extra-region variants

The window layout is one of several ways to add regions to a 9x9, and they're all solved the same way.

• Sudoku X (Diagonal Sudoku) — the two main diagonals each hold 1–9.
• Centerdoku — the center cell of each of the nine boxes forms a tenth region.
• Asterisk sudoku — nine cells arranged in a star shape form an extra region.
• Girandola sudoku — nine cells in a pinwheel pattern around the center form an extra region.
• Jigsaw sudoku — irregular regions replace the boxes rather than supplementing them.

All of these share the key mental shift: a cell's peers are whatever the puzzle says they are, not whatever a classic grid trained you to expect.

Mistakes that cost people windoku puzzles

Nearly every failed attempt at this variant comes from treating the windows as decoration.

• Forgetting the window when pruning candidates. Placing a 6 at R3C3 must clear 6 from that window's other eight cells, not just from the row, column, and box. Miss this and the grid contradicts itself much later.
• Assuming window cells and box cells behave the same. A window overlaps four boxes. The cells it shares with each one behave very differently, and the 4/2/2/1 split is the source of most useful deductions.
• Never checking the hidden regions. They're the difference between an easy solve and a grind.
• Confusing shaded windows with jigsaw regions. In this variant the ordinary 3x3 boxes still apply. Shading adds a constraint; it doesn't replace one.

Other variants to try

• Killer sudoku — cage sums replace most givens, and the counting arguments there rhyme with the region derivation above.
• Colored sudoku — colors instead of digits, and shaded regions are easier to read when the symbols are colors too.
• Giant sudoku — 12x12, 16x16, 25x25 and the Samurai layouts.
• Play 16x16 sudoku online — the same logic across 256 cells.
• 6x6 sudoku — the shortest grid that still teaches crosshatching.
• Sudoku evil — classic 9x9 at the hard end.

For printable classic grids, our free puzzle maker generates 9x9 sudoku at easy, medium, and hard, one to six per page, with an answer key on every sheet.

Frequently asked questions

What's the difference between hyper sudoku and windoku?

None. They're two names for the same puzzle: a 9x9 grid with four extra shaded 3x3 regions at rows 2–4 and 6–8, crossed with columns 2–4 and 6–8. NRC sudoku and four-square sudoku are further names for the same layout.

Are the four windows always in the same place?

Yes, by convention. Every published puzzle of this type uses rows 2–4 and 6–8 against columns 2–4 and 6–8, leaving a one-cell border around the edge and an unshaded cross through row 5 and column 5. If you find a grid with shaded blocks somewhere else, it's a different variant and you should read its instructions.

Is this variant harder than classic sudoku?

Usually easier at the same clue count, and often rated harder because the clue count is lower. Four extra units mean more deductions are available at every stage, so the opening moves faster. The difficulty is a bookkeeping one — you have to remember that window cells constrain each other, and that's an easy habit to lose halfway through.

How many clues does one of these puzzles have?

Often in the low twenties, versus the mid-twenties to mid-thirties typical of a classic 9x9. The extra constraint replaces several givens. There's no proven minimum for the variant the way 17 is proven for the standard grid.

Do the hidden regions really always hold 1 through 9?

Yes, and it's provable rather than observed. Rows 2–4 contain 27 cells and three of each digit; two complete windows sit inside them accounting for two of each digit; so the nine leftover cells in columns 1, 5, and 9 must supply the third of each. The same counting argument produces the other four hidden regions. You can check every one of them against the verified grid above.

Can two cells in different boxes be peers here?

Yes, and that's the whole point of the variant. Any two cells inside the same shaded window are peers, so R2C2 and R4C4 cannot hold the same digit even though they share no row, no column, and no box. Forgetting this is the single most common source of errors.