Selling girandola sudoku puzzle books as downloads: the pinwheel cells your buyer checks one by one, trusting every digit is true

A Girandola book punishes a bad file in a way no sample puzzle ever shows. Your buyer judges puzzle forty-one, when the nine shaded pinwheel cells — scattered across the whole grid, nowhere near each other, the pattern the book is named for — hold a 4 in one far corner cell and another 4 in a shaded cell on the opposite side, because the generator's checker audited rows, columns and boxes and never once gathered the nine marked cells together as a set — or when one shaded cell quietly lost its shading in the layout pass, so the region the solution was built on and the region printed on the page are two different sets of nine, and a perfectly correct deduction now looks like a repeat — or when the centre cell's shading vanished in the print export, so the middle of the pinwheel left the page and only the difficulty stayed. Girandola Sudoku is classic Sudoku plus one scattered region: a 9x9 grid, digits 1 to 9 once in every row, column and 3x3 box, and nine marked cells, forming a pinwheel or windmill pattern across the entire grid — a girandola is a revolving firework — which together must also contain the digits 1 to 9 exactly once. Underneath it is a contract in five parts, each part exact. First, the row rule. Second, the column rule. Third, the box rule. Fourth, the Girandola rule: the nine marked cells are one extra region, a tenth region alongside the nine boxes, and they must hold 1 to 9 exactly once — a full set owed, not merely no repeats. Fifth, closing the contract, given and set integrity with uniqueness: the givens and the marked set are fixed exactly as published, and exactly one completed grid satisfies every part at once, reachable by deduction alone, with no guessing. A puzzle that breaks any part is not slightly harder. It is false as stated. A good Girandola book is a verified stack of sets: every pinwheel re-gathered cell by cell against the printed solution, on the final file, puzzle by puzzle.

Four warnings belong at the front, because they are the mistakes this genre makes most often, and all four start with puzzles Girandola is not. Girandola is not Center Dot Sudoku, its closest named neighbour, in which the nine extra cells are the centre cells of the nine 3x3 boxes — a regular, evenly spaced set that a solver can find without any shading at all: Girandola's nine sit in a pinwheel arrangement that is not the box centres, and a checker that gathers the box centres on a Girandola book has audited nine perfectly respectable cells that are simply the wrong nine, and will pass books whose real pinwheel repeats a digit. Girandola is not Asterisk Sudoku either, where the nine extra cells form a star-shaped cluster centred on the middle of the grid: Girandola's cells are spread across the entire grid, out to its edges, and a buyer hunting only in the middle will miss most of the region they bought. Girandola is not a region variant like Windoku, where the extra units are four whole extra boxes: the Girandola region is nine single cells that share no borders as a block — it has the full-set duty of a region without the shape of one, which is exactly why both checkers and buyers overlook it. And Girandola is not classic Sudoku with decorative shading: the moment a cell is shaded as part of the pinwheel, it binds, and a solution that repeats a digit across the nine shaded cells is wrong no matter how clean its rows are.

The book is every pinwheel cell on every puzzle, not the sample puzzle

Every seller checks the sample. The sample is the puzzle on the listing image, the one in the preview, the one whose nine shaded cells you gathered while the generator was still open. It will be perfect, because you looked at it. The book is the other ninety-nine puzzles — generated in batch, exported in batch, never re-gathered set by set — and in this genre a batch is exactly where the law quietly dies, because the Girandola rule is the easiest Sudoku constraint to forget in a checker: it lives in no row, no column and no box, so every ordinary audit passes straight over it. A classic checker ignores the pinwheel entirely and passes everything. A no-repeat checker is subtler and nearly as dangerous in the opposite direction: it confirms the nine cells merely avoid repeats, which any nine random cells in a valid classic solution will almost do by accident, and it never asks the harder question this genre actually owes — are all of 1 to 9 present among the nine? A checker that gathers the wrong nine — the box centres, the centre cluster — is the third failure, and the worst, because it produces confident reports about a region the book never promised. The only checker that can catch this genre's failures is one that reads the exact marked set as printed, gathers those nine cells, and asks two questions — does any digit appear twice, and is any digit missing? — and if your pipeline never asked both questions set by set, your book's defining rule was enforced by hope.

That is why this genre's reviews, when they turn, turn on trust rather than difficulty. A buyer can forgive a hard puzzle. What they cannot forgive is gathering the nine shaded cells, correctly and patiently, from every corner of the grid, to prove the last empty shaded cell cannot be a 4 — because a 4 already sits in a shaded cell three boxes away, in ink, in the givens — writing in the only digit their logic allows, and discovering the key repeats the 4 in the pinwheel anyway while the missing digit appears in no shaded cell at all. One photographed pinwheel like that outweighs fifty clean puzzles in a review, and it should: the buyer is right, the file is wrong, and the sample puzzle on your listing, however perfect, is not evidence about puzzle forty-one. So the working rule for everything below is simple. The unit of quality is not the book, and it is not the sample. It is the single marked set, verified on the final exported file, after layout, after any reflow, on the exact bytes the buyer downloads.

The contract, part by part

State the contract exactly, the way your rules page should state it, because every audit that follows is just this paragraph with its sleeves rolled up.

Part one, the row rule: each of the nine rows holds the digits 1 to 9 exactly once. Part two, the column rule: each of the nine columns holds the digits 1 to 9 exactly once. Part three, the box rule: each of the nine 3x3 boxes holds the digits 1 to 9 exactly once. These three are classic Sudoku entire, and they are necessary but nowhere near sufficient — a grid can satisfy all three and still repeat a digit across its pinwheel while leaving another digit out of the shaded set altogether.

Part four, the Girandola rule: the nine marked cells, taken together, hold the digits 1 to 9 exactly once. Three consequences follow, and your rules page owes the buyer all three in plain words. First, the duty is the full set, not just no-repeat: nine cells holding eight different digits with one repeated and one missing fail this rule twice over, and your page must say the set must be complete, because a buyer fresh from a no-repeat variant like Argyle will otherwise grade your book by the weaker law — Argyle's short marked lines owe no full set; Girandola's nine-cell region owes all of it, and confusing the two laws in either direction falsifies a book. Second, the marked set is the law: the nine cells shaded in the file are exactly the cells that form the region — no unmarked cell joins the region because it looks like it belongs to the pattern, and no marked cell can be dropped from the law because it sits far from the others. Third, scatter compounds: each marked cell also belongs to its own row, column and box at the same time, and the centre cell sits at the heart of the pattern, so a single wrong digit in a shaded cell can break its row, its column, its box and the pinwheel in one stroke — which is why the audit below reads the marked cells first. And the silence around the law matters as much as the law: a cell that is not marked promises nothing beyond its houses, and your page must never let a buyer believe that every shaded-looking cell in the grid is policed, or that the pinwheel can be guessed from the pattern's name alone.

Part five, given and set integrity with uniqueness: the ordinary givens and the marked set itself are fixed exactly as published — the shading is not decoration, it is part of the puzzle statement, so no cell quietly shaded, unshaded or moved between editions — and exactly one completed grid satisfies parts one through four together, reachable by deduction alone. No guessing, no bifurcation, no "the pinwheel also works the other way round." In a scattered-region genre a second solution often hides exactly in the scatter: two unshaded-by-mistake cells whose digits can swap without touching any house or the true region, which is why uniqueness here must be proven by a solver that enforces the nine marked cells as a region, never assumed from a classic solve.

One more piece of arithmetic belongs in the contract, because the audit leans on it. A complete region of nine cells holding 1 to 9 exactly once excludes each placed digit from the other eight marked cells at once, wherever they sit: placing one digit in a shaded cell removes that digit from eight cells scattered across up to nine different boxes at once, a reach no row, column or box can match. That reach is the genre's engine. It is also its multiplier of mistakes: an error in the marked set itself — one cell shaded a square off in the export — changes the exclusion map of every puzzle in the book, so the printed puzzle and the solved puzzle silently become two different puzzles that happen to share a grid.

Counting the region itself belongs in the contract too, because sellers get it wrong in print. The Girandola set is always nine cells — no more, no fewer: an eight-cell shading cannot hold 1 to 9, and a ten-cell shading cannot hold them exactly once, so a rules page that cannot point to exactly nine marked cells on its diagram grid is describing a book that cannot satisfy its own cover. Your rules page should therefore never say "the shaded cells" as if the buyer could guess which ones: it should show the marked set on a diagram grid, in the same orientation and shading as the puzzles, and it should promise that every puzzle in the book uses that same set unless a puzzle page says otherwise. A buyer who has to infer the region from the first puzzle's givens has been handed homework where a diagram was owed, and a book whose later puzzles quietly change the marked set — a batch generated against a second pinwheel layout and merged in — has broken its contract in a way no single-puzzle check will catch. The audit's set check therefore runs in both directions: file against source, and puzzle against puzzle across the whole book.

The verification audit: eight checks before any file ships

Run all eight on the final file, per puzzle, in this order. The audit assumes nothing from generation; it re-reads the page as the buyer receives it.

1. House recount. For the printed solution, recount every row, column and box: nine distinct digits, 1 to 9, no repeats, no omissions. This is the classic pass, and it is only the entry fee.

2. Pinwheel full-set recount. Gather the nine marked cells exactly as printed and confirm they hold 1 to 9 exactly once — no digit twice, no digit missing. Not a spot check, not the shaded cells near the centre only — all nine, every puzzle. This single check is the genre; a checker that only audits houses has failed to run it, and the difference is precisely the repeated 4 sitting in two shaded cells on opposite sides of a grid that "looked fine."

3. Marked-set audit. Read the shading in the final file against the source puzzle, cell by cell: every intended cell shaded, no extra cell shaded, no cell shaded one square off after a layout pass. In this genre the marked set is law, so a shading defect is a rules defect: a pinwheel cell that lost its shading in the PDF is a constraint the buyer cannot see and cannot be blamed for misreading.

4. Wrong-nine sweep. Confirm the checker and the rules page never gathered a different nine: not the box centres of Center Dot, not the central star of Asterisk, not any nine convenient cells. Re-read the audit configuration and the page copy, and strike any test that grades a set the book never promised. This is the genre's signature false pass, and a book "verified" under it has not been verified at all.

5. Given-agreement sweep. Diff the printed givens against the source puzzle cell by cell, and confirm every given that sits in a marked cell agrees with the marked set as printed — a given moved one cell by a reflow can land outside the pinwheel the solution was built against, and no house check will ever notice.

6. Uniqueness under the real rules. Re-solve each puzzle with a solver that enforces rows, columns, boxes and the nine marked cells as a full region, and confirm exactly one solution, reachable by deduction without guessing. A classic-only solver is not evidence here: it will happily certify puzzles that have a second solution hiding in the scatter.

7. Stray-law sweep. Confirm nothing unmarked is being enforced and nothing marked is being ignored: no solution may be failed for repeating a digit across an unmarked set the key notes invented, and no marked cell may be excused as "only a guide." The file's shading and the file's law must be the same set, in both directions.

8. Printed-proof solve. Solve one puzzle per difficulty band from the printed file itself — paper or the delivered PDF at reading size — gathering the nine shaded cells by eye as a buyer would. Shading too faint to spot at reading size, a shaded cell that reads as a printing smudge, and digits that vanish against the shading are failures this check exists to catch, because the buyer will catch them in a review instead.

A book that passes all eight earns its rules page. A book that skips check two has not been audited at all, whatever else was run — it has only been proven to be a classic Sudoku book with shading drawn on it.

Difficulty is how hard the pinwheel works, not how few givens you printed

Given count is the laziest difficulty metric in Sudoku, and in Girandola it is close to meaningless. Two puzzles with identical given counts can sit at opposite ends of honest difficulty, because what makes a Girandola puzzle hard is not how many cells start empty but how much work the scattered region does: how often the decisive deduction is a pinwheel exclusion reaching across the grid rather than a house exclusion next door, and how early the solve is forced to gather nine cells that share no neighbourhood. A puzzle whose pinwheel never decides anything is a classic puzzle wearing the shading as costume — sellable, perhaps, but not the book the cover describes, and buyers who came for the variant can tell by puzzle ten. A puzzle whose every step runs through one shaded cell is a bottleneck, not a challenge: it reads as a trick repeated until it opens.

Grade instead on four things you can measure. First, pinwheel-decision share: in a solver's step log, what fraction of placements were forced by the marked region rather than by a row, column or box. Second, scatter reach: how many boxes the decisive pinwheel deductions cross, and how often the forcing shaded cell sits far from the cell it forces. Third, centre load: how early and how often the solve is forced through the centre cell and the marked cells nearest it, where the pattern's pressure concentrates. Fourth, classic depth underneath: the ordinary solving techniques the puzzle still demands once the region has done its work, so an "expert" label is not carried by one scattered gimmick over an otherwise trivial grid.

Then hold the listing honest against the grades. The sample puzzle on the listing should sit at the book's true median — not the easiest puzzle, polished, and not the hardest, weaponised. State the region in the listing in plain words: that nine marked cells scattered across the grid form one extra region that must hold 1 to 9 exactly once. Buyers of variant Sudoku shop by law, not by artwork; the seller whose listing states the law exactly is the seller whose reviews talk about difficulty as a preference instead of as a surprise. And never grade with a no-repeat assumption hiding in the tooling: a difficulty engine that treats the pinwheel as merely no-repeat will call puzzles solvable that are not, and unsolvable-looking puzzles that are merely waiting for the missing-digit deduction, and the grades will drift from the buyer's experience in exactly the direction that produces "not as described."

Print honesty: the law is printed as nine shaded cells, the first thing a bad export kills

In Argyle the law is printed as thin lines; in Girandola it is printed as nine shaded cells scattered across the grid, and scattered shading is the most fragile ink in any puzzle book. A shaded cell that prints at full strength on your screen can drop out on a toner-saving setting, fade to invisibility at the grid's far corner on a home printer, or alias into a grey smudge a tablet zoom reads as dirt — and every one of those failures deletes law from the page while leaving the puzzle's difficulty fully intact. The buyer is then solving a harder, different puzzle from the one the key answers, and no errata note that says "the shaded cells are the usual ones" fixes a page where the buyer cannot tell which nine cells are marked.

So the print rules are mechanical. Shade every marked cell at a weight and tone that survive a bad photocopy: test the actual delivered file on the worst output you can find, not the best screen you own. Keep the pattern findable — the nine cells must read as one deliberate set, never as random grey noise, and a buyer should be able to count exactly nine without a magnifier: if they count eight or ten, the page has failed before the puzzle has begun. Keep digits legible inside shaded cells: a given printed over shading that swallows its strokes turns reading the given into guessing it. And give the buyer a fallback: a rules page that describes the marked set precisely enough — a diagram grid with the nine cells shown — that a buyer whose print faded can reconstruct the law without writing to you. If the pattern is the standard pinwheel, say so and show it; if a puzzle's marked set differs, flag it on that puzzle's page, never silently.

The solution key carries the same duty. Print the key with the same nine cells shaded at the same strength as the puzzle page, large enough that a buyer disputing the region can gather the nine key cells themselves and count 1 to 9 across them. A key that drops the shading — common in batch exports, where the key is rendered from the solution grid alone — makes every pinwheel dispute unanswerable from the book itself, and unanswerable disputes become reviews. The genre runs on gathered sets; the whole book, givens, shading and key, must be gatherable end to end.

Licensing, provenance, and whose variant this is

Girandola Sudoku is a modern variant in the public Sudoku tradition: the rules themselves — classic houses plus one scattered nine-cell region holding 1 to 9 — are a published convention used by setters and championships, not a private invention you license or a brand you borrow. The name itself is the Italian firework the pattern is named for, shared variant culture, not a trademark you are borrowing. What you may not borrow is other people's puzzles, other people's marked layouts presented as their authored sets, and other people's artwork. Generate your own puzzles, shade your own grids, and keep the generation record: the software or method, the marked set used, the audit output per puzzle. That record is your provenance if a marketplace ever asks, and it is your errata map when something slips through.

State your licence terms for the buyer plainly, the way the honest sellers in this niche do: personal use, print for your own solving, no redistribution of the file. If you allow classroom or club printing, say how many copies and for whom; silence on the point does not protect you, it just guarantees the keenest buyers — teachers and club organisers, often your best repeat customers — will either ask and wait, or walk. And keep one rule for yourself above the licence text: never lift puzzles from a free puzzle site, a newspaper, or another seller's book to fill a slow volume. The variant community is small, pinwheel layouts and given patterns are fingerprints, and a single recognised puzzle ends the trust the audit was built to create.

Corrected-file delivery is the promise that closes the loop. When an error does slip through, the fix is not a quiet re-upload that leaves early buyers holding a false book: it is a corrected edition, a note saying which puzzle changed and why, and the new file pushed to every buyer of the old one. I run my own delivery for books like these through FileFreight, which exists for exactly this unglamorous job — flat-rate delivery of the file, license keys where a book needs them, and a corrected edition reaching the people who already paid, not only the people who buy tomorrow. Whatever tool you use, hold it to that standard: if your delivery cannot re-serve a corrected file to past buyers, your errata policy is a sentence you cannot keep.

The launch checklist

1. The rules page states the contract in five parts, says the nine marked pinwheel cells form one extra region, states that region must hold 1 to 9 exactly once, and shows the exact marked set on a diagram grid.
2. Every puzzle was audited on the final exported file: houses recounted, the nine marked cells gathered and confirmed complete 1 to 9, and the shading diffed against the source, cell by cell.
3. Uniqueness was proven by a solver that enforces the marked region, and no puzzle in the book needs guessing.
4. Difficulty grades come from how hard the pinwheel works — decision share, scatter reach, centre load, classic depth — not from given count, and the listing sample sits at the book's true median.
5. The delivered file was print-tested on poor output: exactly nine shaded cells are countable at reading size, digits stay legible over the shading, and the key prints the same nine cells shaded.
6. Puzzles, grids and artwork are your own generation, with the generation record kept; licence terms state personal use and any classroom or club allowance in plain words.
7. A corrected edition can be re-served to every past buyer, with a note naming the puzzle that changed — and the delivery tool you use was held to that standard before the first sale, not after the first complaint.