Jigsaw Sudoku strategy: read the region that is really there

One replacement changes the map

A familiar 9×9 outline can make your eye invent boxes that the puzzle no longer has. In Jigsaw, also called irregular Sudoku, follow the printed regions. Each region contains nine cells and needs the nine different digits; rows and columns remain active. The ordinary 3×3 partition is replaced. [1]

Thomas Snyder’s published Jigsaw puzzle expresses the rule using rows, columns and bold regions, rather than requiring square blocks. [2] That wording matters. Two cells in the old upper-left square may belong to different regions. Conversely, cells several rows apart may share a long, bent region.

Before writing notes, trace a single border from start to finish. If an outline is hard to follow, identify its protruding cell or narrow neck first. A temporary region letter is often more useful than trying to describe its shape every time.

An original map you can inspect

The repeated letters in this diagram deliberately make membership explicit. Region A contains the top-left three cells, followed by two cells in each of the next three rows. Counting 3+2+2+2 confirms its size. Its outline crosses where a standard horizontal box boundary would have been.

For any selected cell, name its row, its column and its one labelled region. Those are the three houses to check. A thick edge is a constraint boundary, while an imagined square is not. The classic row and column rules still operate as described by Nikoli. [3]

A region single uses familiar logic

Suppose a region is missing {2,5,8}, with three empty cells A, B and C. A and B are in row 4, while C is in row 6. If row 4 already contains 5 outside that region, A and B cannot take 5. Therefore C is the region’s only remaining 5.

The region may be a hook, a staircase or an unfamiliar shape; the proof is unchanged. Notice also what is still unknown: A and B remain {2,8} unless a further restriction distinguishes them. Do not convert a useful regional deduction into an unsupported guess about its neighbours.

A naked single asks which digits fit one cell. This hidden single asks which cells fit one digit in a region. Switching the direction of that question is useful when a region has several empty cells but one particularly restricted digit.

The shape can trap a digit in a line

Now assume every surviving 6 in region A lies at r1c1 or r1c2, where r1c1 means row 1, column 1. Region A must contain 6 somewhere. Both possibilities are in row 1, so the rest of row 1 cannot contain another 6. The diagram marks those outside eliminations with crosses.

The reverse direction can also work. If all candidates for a row’s 6 lie inside one irregular region, remove 6 from the rest of that region. In either direction, verify the word “all”. One forgotten candidate on a distant protruding cell breaks the proof.

Update a whole region after a placement

After entering a digit, clear that digit from its row, column and entire irregular region. The far end of a long region is easy to overlook. This is where tracing once more is more valuable than making a faster scan of the familiar-looking centre.

Do not assume an irregular region is an ordinary box plus a few decorative extensions. Likewise, do not apply an advanced square-box pattern without checking whether its proof depends on the three-by-three arrangement. Singles and all-different sets transfer naturally; geometry-specific shortcuts need a fresh argument.

A useful paper exercise is to choose a region and list its nine coordinates. Then compare that list with the candidate notes you updated. You are testing membership, not solving speed.

Region boundaries can also show why an apparently familiar pair does nothing useful. Two cells with candidates {3,7} form an eliminating pair only within a house they both share. If they merely sit inside the same imagined square, while occupying different rows, columns and actual regions, they do not reserve 3 and 7 anywhere together. Point to the shared house before removing candidates from its other cells.

Keep the extra rule out of your imagination

The current ZUDOKU Jigsaw page displays a Plus preview. These diagrams and questions can be used directly without treating that preview as a playable practice board. For a complete published puzzle, follow the constructor’s source below and read its own rules.