🔷 Jigsaw Sudoku Puzzles

Jigsaw Sudoku: Sudoku With the Boxes Bent Out of Shape

Take an ordinary Sudoku and rub out the nine square boxes. Now draw nine new regions of nine cells each, in whatever shapes you like, so long as each one is a single connected blob. That is Jigsaw Sudoku, and it is the most quietly interesting thing you can do to a Sudoku grid without adding a single new symbol. Everything you already know still applies — and one thing you almost certainly don't know suddenly becomes the most powerful move on the board.

📏 The Rules, All of Them

There are three, and you know two already:

• Every row holds each digit exactly once.
• Every column holds each digit exactly once.
• Every region — the shaded, outlined blobs — holds each digit exactly once.

That's it. On the 9 × 9 board the digits are 1 to 9 and there are nine regions of nine cells; on 6 × 6 it is 1 to 6 in six regions of six; on 4 × 4, 1 to 4 in four regions of four. The regions are always connected edge to edge — you can walk from any cell of a region to any other without stepping outside it — and every region on the board gets a shade of its own, so two blobs the same color are never two halves of the same thing.

The regions are drawn fresh for every puzzle, by swapping cells across their borders in pairs so the sizes hold steady while the shapes wander. They are never simply the square boxes: a 9 × 9 layout here runs to about 62 cell-to-cell borders between different regions, against 36 for square boxes — nearly twice the edge, which is what makes them look like jigsaw pieces.

🔄 What Changes When the Boxes Stop Being Boxes

A square box does a lot of quiet work in ordinary Sudoku: it always meets exactly three rows and exactly three columns. Every intersection technique you have ever used — pointing pairs, box-line reduction, the whole family — leans on that tidy arrangement.

An irregular region does not play along. It can stretch across seven rows, hug a single column for six cells, or fold round a corner so two of its own cells sit diagonally opposite with none of the region between them. Some of your habits get weaker as a result. One gets much, much stronger.

🎯 Where to Start: Scan the Squiggle, Not the Square

In ordinary Sudoku you scan a box and ask "where can the 4 go in here?", sweeping your eyes along three rows and three columns. Do the same thing here, but scan the region, and let its shape tell you which lines to sweep.

Pick a region and count how many of its cells sit in one row. If five of a region's nine cells are strung along a single row, five of that row's digits are locked inside that region and only four are anywhere else — a huge amount of information, and one with no equivalent in a 3 × 3 box, where the answer is always three.

The same is true in reverse. A region that reaches into six different rows is weakly tied to all of them and is usually the last one you should look at. Compact regions and long straight regions are where the puzzle opens; sprawling ones are where it closes.

✂️ The Law of Leftovers — The Move That Only Exists Here

This is what the 9 × 9 Hard puzzles are built around, and almost nothing else in puzzling works quite like it. Take the top two rows of a 6 × 6 grid: between them they hold each of the digits 1 to 6 exactly twice. Now take any two whole regions — they also hold each digit exactly twice. Two collections, same contents.

So if the two regions almost — but not quite — fill the two rows, the mismatch has to balance. Whatever part of the rows the regions failed to cover must contain precisely the same digits as the part of the regions that spilled outside the rows.

That is the Law of Leftovers, and it scales: three rows against three regions, four against four, columns just as well as rows. When each side is two cells rather than one you don't get an equality, but you still get a pruning — a digit that can't appear anywhere on one side can't appear on the other either.

🔍 Two Techniques That Carry Straight Over

Singles, in all three directions. If a cell has only one digit left, write it. If a region still needs a 7 and only one of its nine cells can take one, that's your 7. Nothing changes here except that "region" has an odd shape — and the odd shape is what makes them easy to miss, because your eye no longer sweeps a neat square.

Locked candidates. If every place a 3 could go inside one region happens to sit in the same row, then the 3 for that region is somewhere on that row, so it is nowhere else on that row. Same trick as in ordinary Sudoku, and it works exactly as well — but with irregular regions it fires less often, because a region's cells are usually scattered over more rows than a box's are. Don't expect it to carry you as far as it does in a normal grid.

⚠️ Three Mistakes Sudoku Players Make Here

1. Trusting the shape of your eye. In ordinary Sudoku you check a box by glancing at a square; here you have to trace the outline. The commonest error on this board is writing a digit that already sits in the same region, two cells away round a corner, where you never looked.
2. Treating a region as roughly a box. A region reaching into seven rows is a different object entirely, and any reasoning that assumes "three rows, three columns" quietly breaks.
3. Ignoring the leftovers because they feel like cheating. The Law of Leftovers links cells that share nothing, which feels wrong the first few times. It isn't. It is just arithmetic, and on a hard grid it is often the only door.

🎚️ What Easy, Medium and Hard Actually Mean Here

Difficulty on this page is defined by the techniques a puzzle needs, not by how many digits we felt like removing. A clue only comes off the grid if a solver that knows the techniques on this page can still finish without it — which is also why every puzzle here has exactly one answer, and why you never have to guess.

Measured over 405 generated puzzles. "Given" counts the digits printed at the start.

Two honest notes on that table. First, the 9 × 9 Hard promise is checked rather than hoped for: before a Hard puzzle is published, a solver armed with everything except the Law of Leftovers is set loose on it, and the puzzle is only kept if that solver fails. Across the last test run that held for 45 out of 45. To put it another way, on a 9 × 9 Hard a solver that knows only singles grinds to a halt with about 59 of the 81 cells still empty.

Second, the smaller boards do not make that promise, and we are not going to pretend otherwise. Sixteen cells and four digits leave no room for the idea at all: not one 4 × 4 grid in two hundred needed it. Six-by-six manages it about three times in a hundred, which is too rare to build a level on. So 6 × 6 Hard asks the same techniques as 6 × 6 Medium — both are checked to need more than singles — and simply gives you less to go on. On the 4 × 4 board nothing is gated at all: all three levels can be finished with singles alone, and Easy, Medium and Hard differ only in how many digits you start with. It is a board for learning the shapes on, not for being beaten by.

🎮 Playing on This Page

Tap any empty cell and a keypad appears offering only the digits it can still legally take. Or use the keyboard: arrows to move, a digit to write, Backspace to clear. On a phone the number bar under the board acts on the selected cell.

Notes (or the N key) switches to pencil marks. There the keypad offers every digit rather than only the legal ones, because writing down a maybe is the entire point, and it stays open while you jot so a whole set goes in at once. Writing a real digit clears that cell's own marks and nothing else — your working elsewhere is never wiped for you. Selecting a cell tints the rest of its region, the quickest way to see a shape you can't trace by eye, and clashes light up in red as you make them.

📜 Where Jigsaw Sudoku Came From

The puzzle goes by a small pile of names: Irregular Sudoku, Squiggly Sudoku, Geometric Sudoku and Nonomino Sudoku. The last is the precise one — a nonomino is a shape made of nine connected squares, which is exactly what the nine regions of a 9 × 9 jigsaw grid are.

The American puzzle designer Bob Harris developed and published his own irregular-region puzzles under the name Du-Sum-Oh, and he is the one who named the Law of Leftovers. It is a rare thing in puzzling: a technique that belongs to one variant and one variant only, with a known author.

🧒 A Good First Variant for Younger Solvers

If someone is comfortable with a small Sudoku and you want to hand them something new without teaching a new rulebook, this is the one: no sums, no inequalities, no extra symbols, and yet the board feels completely different. The 4 × 4 grid is genuinely gentle — four digits, four little shapes, seven of the sixteen cells already filled in on Easy, and colors to follow rather than an outline to trace. It also builds a habit worth having: checking a group by its real boundary instead of by where you expect the boundary to be.

🚀 Give It a Go

Start on 6 × 6 Easy if the shapes are new to you, or go straight to 9 × 9 Medium if you solve ordinary Sudoku without thinking. When you get to 9 × 9 Hard and the singles dry up, come back to the diagram above and count rows against regions — that's the door. 🔷