Thirty-six squares, and a box that isn't square
The rules survive the shrink intact. Every row holds 1 to 6, every column holds 1 to 6, every box holds 1 to 6, and nothing repeats. What cannot survive is the shape of the box. Nine splits neatly into three threes, so a standard grid tiles with squares; six does not split into equal squares at all, so a mini grid is carved into six blocks three squares wide and two tall. That asymmetry is the first thing to notice and the easiest to forget: two boxes sit side by side across the width, three sit stacked down the height, and a horizontal sweep therefore crosses a box boundary in a different rhythm from a vertical one.
Count what that leaves. A square here is watched by twelve of the thirty-five others, better than a third of everything on the board. On a standard grid a square is watched by twenty of eighty, a flat quarter. Proportionally, every placement you make on a mini grid reaches further than the same placement would on a big one, and the effect compounds: fill one square and you have meaningfully narrowed a third of the puzzle. This is the real reason mini grids feel fast. It is not that there are fewer squares to fill. It is that each square you do fill does more work.
The same density shows up in the count of grids. We put our own solver to work enumerating every legal completed 6×6 arrangement and it found 28,200,960 of them — a number you could store in a spreadsheet column if you were determined. The equivalent count for a 9×9 grid, worked out by Bertram Felgenhauer and Frazer Jarvis in 2005, runs to twenty-two digits. Mini sudoku is not a smaller version of the same space. It is a different order of thing.
The techniques a small grid never gets round to
Here is where a mini grid stops being merely quicker and starts being genuinely different. Anyone taught sudoku in the usual order learns singles first, then naked and hidden pairs, then locked candidates, and only afterwards the patterns that stretch across the whole board. On six by six, that middle rung barely exists. We dug four thousand grids at nine clues apiece and graded every one by replaying it with the same ladder of human techniques that grades every board on this site. Only 215 of the four thousand needed anything beyond a single. Of those 215, just twelve topped out at locked candidates and precisely two at a subset.
Why the pairs and triples don't get their turn
A naked pair is two squares in one house that between them admit only two digits, which lets you strike both digits from everything else in that house. Notice what the technique needs to be worth anything: a house with several squares still open, at least two of them narrowed to the same two candidates, and other open squares left over to eliminate from. A house here has six squares. By the time two of them are down to two candidates each, the house is usually so short of options that some square in it is already a single — and our grader, which always takes the gentlest move available, records the single instead. Subsets are not absent from these boards; press the Hint button often enough and one will be offered to you. What almost never happens is a puzzle whose hardest required step is a subset, and that is the thing a level is measured by.
What turns up instead
The puzzles that do resist singles mostly step straight over the middle of the ladder and land on patterns spanning the grid. Three quarters of our 215 were a skyscraper or an XY-wing — deductions that follow one digit across two lines and pinch off a square neither line touches directly. Those thrive on exactly what makes subsets fail. A short line makes it far more likely that a digit has only two homes left in it, and two homes in each of two lines is the entire raw material of a skyscraper.
Fewer squares in a house means fewer places for a digit, and a digit with two places left is where the interesting patterns start.
None of this is a special mini technique that we invented for the page. It is the same skyscraper you would meet on an expert 9×9 board, found by the same code, described in the same words by the same Hint button. What has changed is how often the position hands it to you. If you have been meaning to learn the single-digit patterns and have found them elusive on a full grid, a run of hard mini puzzles is the most concentrated practice we can offer: the pattern is short enough to see whole, and it turns up in almost every puzzle that isn't pure singles.
Three levels, and an honest reason there is no fourth
The selector above offers Easy, Medium and Hard. It stops there, and it stops there on purpose. Easy grids start with sixteen clues and never ask for more than a naked single; Medium grids start with ten and always need at least one hidden single; Hard grids start with nine and always need something above both. Because the top band lands on a different pattern from one puzzle to the next, it does not repeat a fixed promise — the line above the board names whatever technique that particular grid genuinely requires, whether that turns out to be a skyscraper, a wing, or something rarer.
A fourth level would need somewhere further to go, and there is nowhere. Two ceilings close in at once. The first is arithmetic: strip clues from a 6×6 grid as aggressively as the digger can and it settles around ten, reaches nine often, and touched eight ten times in three thousand attempts. Past that point a removal nearly always admits a second answer, and a puzzle with two answers is not a hard puzzle, it is a broken one. The second ceiling is the ladder itself, for all the reasons above. We could print a fourth chip on the selector easily enough. We could not make it mean anything, so it isn't there.
What we get in exchange is speed. A whole search for a Hard mini grid — up to seventy candidate puzzles, each one dug clue by clue with a fresh proof of uniqueness after every removal, then replayed technique by technique — finishes in about twenty milliseconds on an ordinary laptop. Pressing New puzzle here is instant in a way it never quite is on the diagonal or jigsaw boards, where a single grid can take the best part of a second to justify.
What a small board is actually good for
Two audiences, and they want opposite things from it. Someone learning gets a grid where the whole logical situation is visible at once: no need to write candidates in twenty squares to see a pattern in three, and a mistake shows up within a move or two instead of twenty minutes later. Someone experienced gets a puzzle that fits in the gap between two other things — a queue, a kettle, a train pulling in — and, on the Hard setting, concentrated exposure to the one family of techniques that a full grid rations out.
Everything the standard board does, this one does at six. Pencil marks arrange themselves two rows of three inside each square instead of three by three. The number pad runs 1 to 6 and keeps its count of how many of each digit are still to place. The Hint button names the deduction rather than handing over a digit, the share link carries the grid itself so it works with no account and never expires, and your game is stored under its own key, so a puzzle you start here survives a trip to the full-size board and back. The pack builder above prints the same grids as vector artwork, boxes three wide and two tall in heavier rule than the rest, with answers at the back.