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Irregular Sudoku

Irregular Sudoku, also called jigsaw Sudoku, replaces the nine 3×3 boxes with nine irregularly shaped regions of nine connected cells each, while rows and columns work as usual. Every row, column and region must hold each digit once. The layout of regions changes from puzzle to puzzle.

The board offers all five levels, with 49 Easy, 80 each at Medium, Hard and Expert, and 45 Evil puzzles stored.

How do jigsaw regions work?

Each region is a connected shape made of nine cells. The nine regions together cover the whole board with no gaps or overlaps, and each must contain the digits 1 to 9 once. A region might be a long snake across several rows or a compact blob. The layout is part of the puzzle, so a new puzzle usually means a new map. The rules page places this beside the other variants, and the controls page covers input.

The first job in every puzzle is to read the map. In the game, region boundaries are drawn on the board, and the hint text refers to regions by number, such as “region 4”. Take a few seconds to trace the shape of each region before you begin, because it is easy to assume a cell belongs to a region that it merely touches.

Where do the layouts come from?

Layouts are generated offline. The generator starts from nine horizontal stripes of nine cells and repeatedly swaps boundary cells between neighboring regions, keeping each region connected and exactly nine cells in size. It then tries to build a valid grid for that layout. Some layouts admit no valid grid and are discarded. Every stored puzzle is verified to have exactly one solution for its own layout, as described in how puzzles are generated and verified unique.

How many givens do puzzles have?

Between 14 and 22, averaging 18 to 19 across the levels. That is well below the classic board’s 24 to 25. Here too the clue count says little about difficulty, since the levels have similar averages.

Why do box and line interactions matter so much here?

On the classic board the regions are square boxes that line up neatly with rows and columns. Jigsaw regions cut across them at odd angles, so a region and a row or column often share two or three cells in an irregular pattern. That makes the interaction techniques much more common. In the stored data:

The practical lesson is that pointing pairs and box/line reduction are not optional extras on this board. They are the main workhorses from Medium on, and the X-Wing is needed in most Hard puzzles. The two techniques work the same way as on the classic board, with the region taking the place of the box.

Do the other techniques still apply?

Yes. Rows and columns are ordinary, so techniques built on rows and columns, such as X-Wing and Swordfish, carry over unchanged. Techniques that work within a house work within each region. The unique-rectangle shortcut also works, because the board has no extra constraints beyond rows, columns and regions, and every Evil puzzle here depends on it. A rectangle must still sit in exactly two regions for the shortcut to be safe, which you can check from the map.

A solving routine for jigsaw puzzles

  1. Trace each region and note its shape and any cells where it meets a long row or column.
  2. Start with the digits that are already placed most often, and look for hidden singles in regions as well as rows and columns.
  3. Write notes when singles run out, and look at where a region’s candidates for a digit lie along a single row or column.
  4. Check the same thing in the other direction: where a row’s candidates for a digit all lie inside one region.
  5. Look for X-Wings on rows and columns, which are unaffected by the odd region shapes.

How is it different from the other boards?

Compared with diagonal, hyper and killer, which add houses or sums, this board changes the shape of existing houses. It is also one of the few variants with an Evil level. If you want to see where it sits in the range, the games hub lists every board, and the complete solving guide describes each technique in order.