Jigsaw Sudoku: A Friendly Walkthrough

Jigsaw sudoku looks like the regular puzzle has been put through a shredder. The grid is still nine by nine, the digits are still one through nine, but the boxes are no longer three-by-three squares. Instead they are irregular shapes that meander across the board, each one nine cells long, looking nothing like the others.

Once you adjust to the visual chaos, jigsaw plays almost exactly like classic. Every row contains 1 to 9. Every column contains 1 to 9. Every region contains 1 to 9. The only thing that changes is the shape of the region.

What changes about the strategy

The irregular regions break two assumptions that classic sudoku leans on. First, your eye stops finding boxes automatically. You have to consciously trace where one region ends and the next begins. Second, the box-line interactions that fuel pointing pairs and box-line reduction behave differently because the box-line overlaps are different in every region.

Naked singles, hidden singles, naked pairs and hidden pairs all work the same. The mechanics of those techniques do not depend on the box shape, only on the existence of a region. They fire just as often.

Reading the regions

Most jigsaw grids colour the regions or shade them. If you are playing in black and white, trace each region with a pencil outline before you start solving. The few seconds of upfront work save minutes of confusion later. You should never have to ask mid-puzzle which region a cell belongs to.

The "long region" trick

Some jigsaw regions are long and thin: a region that stretches across six columns is common. Long regions interact with rows and columns much more than compact regions do. If a region touches seven different rows, then once seven of those rows have a digit placed, the region's options for the eighth row are extremely constrained.

Look for the longest regions first. They give up placements faster than the compact ones because they share more of the row and column constraints already on the board.

A worked moment

Imagine a region shaped like a backwards L, occupying the top row of the grid and the left three cells of row 2. The region has nine cells across two rows. If row 1 already has 1, 2, 3, 4, 5, 6 placed, the region needs to put 7, 8 and 9 somewhere in those nine cells. Three of the cells are in row 2. Whatever row 2 lacks among 7, 8 and 9 must go in that region. That kind of cross-region reasoning is the heart of jigsaw.

Where it gets hard

Jigsaw puzzles with very irregular regions can be unforgiving in the middle of the solve. Once the first ten or fifteen placements are done, you sometimes face a wall of cells where every region has roughly the same five candidates left, and singles dry up. That is the moment to pencil-mark and look for the same pairs and pointing patterns you would in classic.

One thing that is more useful in jigsaw than classic: looking for a digit's possible homes across all nine regions at once. The region geometry can force a digit into a particular region even when the row and column constraints alone would not.

When to play it

Jigsaw is a refresher when classic feels stale. The visual change forces your eye to work, which makes ordinary techniques feel new again. It is also forgiving to beginners who already know the classic rules; nothing new to learn, just a different shape.

Try one on the jigsaw sudoku page, or browse the rest of the variants if you would like a wider tour: variants catalogue.