How to play jigsaw sudoku
Rules, the Law of Leftovers technique, and solving strategies for every difficulty level. Also covers squiggly sudoku, irregular sudoku, and nonomino sudoku (same puzzle, different names).
What is jigsaw sudoku?
Jigsaw sudoku (also called squiggly sudoku or irregular sudoku) uses a 9×9 grid split into nine regions, just like regular sudoku. The difference is that these regions are jagged, irregularly shaped pieces instead of neat 3×3 squares. Each region contains exactly 9 cells, and the shapes change from puzzle to puzzle.
The mathematical name is nonomino sudoku because each region is a nonomino: a polyomino made of 9 connected cells. Some publications also call it geometric sudoku. All five names refer to the same puzzle with the same rules.
Rules
- Fill every cell with a digit from 1 to 9.
- Each row contains 1–9 exactly once.
- Each column contains 1–9 exactly once.
- Each irregular region contains 1–9 exactly once.
Rules 1 through 3 are identical to standard sudoku. Rule 4 replaces the standard 3×3 box constraint with the irregular region constraint. That single change transforms how you approach the puzzle.
How regions work
In standard sudoku, every puzzle has the same nine 3×3 boxes. You can tell which box a cell belongs to by its row and column coordinates. In jigsaw sudoku, the regions are different in every puzzle. A region might stretch across five rows, curve around the center of the grid, or form an L-shape along the edge.
Our grid marks regions with two visual cues: distinct background colors (9 pastel hues) and thick borders (2–3px) along edges where neighboring cells belong to different regions. Within a region, cells share the same color and are separated by thin (1px) borders.
The key difference for solving: you can't do the mental "row divided by 3, column divided by 3" shortcut to identify a region. You have to visually trace each region's boundary. This is slower, but it's also what makes jigsaw sudoku a genuine step up from the standard version.
The Law of Leftovers
This is the signature technique of jigsaw sudoku. It doesn't exist in standard sudoku because it relies on regions having irregular shapes.
The basic idea
Take any band of three consecutive rows (rows 1–3, 4–6, or 7–9). In standard sudoku, three 3×3 boxes fit perfectly inside each band. In jigsaw sudoku, the regions don't line up with the rows. Some cells from a region sit inside the band, and other cells from that same region spill below (or above) it.
Here's the insight: the band of three rows contains exactly 27 cells and must collectively hold exactly three complete sets of digits 1–9. The regions that overlap the band contribute some of their digits inside the band and some outside it. The digits that "spill out" of the band from one region are exactly compensated by digits from other regions that "spill in."
In concrete terms: if region A has 2 cells below the band, and region B has 2 cells inside the band that aren't part of region B's main body (which sits above the band), then those 4 cells form two matched pairs. The digits in region A's spill-out cells must be the same set as the digits in region B's spill-in cells.
When to use it
Look for regions where most cells sit inside a row band but 1–3 cells extend beyond it. The fewer cells that spill, the more constrained the leftovers are. If only one cell spills out and one spills in, you know they hold the same digit. That's effectively a free placement.
The Law of Leftovers is most useful at hard difficulty and above. At easy and medium, you can usually avoid it. But from hard onward, there are puzzles that cannot be solved without it. It's worth practicing on a few hard puzzles before moving to expert.
Strategies by difficulty
Easy
Scanning and naked singles. Check rows, columns, and regions for cells with only one possible digit. The high number of givens (36–45) keeps things straightforward.
Medium
Add hidden singles. For each unfilled digit in a region, check if it can only go in one cell. The irregular shapes make this harder to spot because regions span more rows and columns than a 3×3 box.
Hard
Naked and hidden pairs, plus the Law of Leftovers. When two cells in a region can only hold the same two digits, those digits are locked to that pair and eliminated from other cells in the region, row, and column.
Expert
Pointing pairs across region boundaries, X-Wings, and chain techniques. Pointing pairs work differently in jigsaw sudoku because a region might intersect a row in non-contiguous cells, creating elimination patterns that don't occur in standard sudoku.
Einstein
All techniques above, applied rigorously. Every puzzle at this level is solvable through logic alone. The generator verifies this before including the puzzle. If you get stuck, the solving path exists; you just haven't found it yet.
Jigsaw sudoku vs regular sudoku
| Feature | Jigsaw Sudoku | Regular Sudoku |
|---|---|---|
| Regions | 9 irregular shapes (different per puzzle) | 9 fixed 3×3 boxes (same every time) |
| Unique technique | Law of Leftovers | Box/line reduction (fixed geometry) |
| Difficulty | Higher at same level due to region tracing | Baseline |
| Visual scanning | Must trace each region's boundary | Neat grid lines, instant box identification |
| Replayability | High (unique layout per puzzle) | Moderate (same structure, different digits) |
Frequently asked questions
Is jigsaw sudoku the same as squiggly sudoku?
Yes. Jigsaw sudoku, squiggly sudoku, irregular sudoku, nonomino sudoku, and geometric sudoku all describe the same puzzle. The name depends on the publisher and country.
Is jigsaw sudoku harder than regular sudoku?
Usually yes, especially at harder difficulties. The irregular regions prevent box-scanning shortcuts and introduce the Law of Leftovers. At easy difficulty the gap is small. At expert and einstein, expect solve times 20–50% longer than standard sudoku at the same rating.
What is the Law of Leftovers?
A technique unique to jigsaw sudoku. When a region overlaps with a band of rows, the digits from cells spilling outside the band must match the digits from other regions' cells spilling into the band. Detailed walkthrough above.