What is the law of leftovers in Jigsaw Sudoku?

The law of leftovers compares a band of rows or columns against the irregular regions that overlap it. Because both the band and the regions must each hold complete sets of 1-9, any cells that stick out of the band must contain the same multiset of digits as the cells of the band that are not covered by those regions. This lets you force exact digits in the 'leftover' cells, and it is the signature technique of Jigsaw Sudoku.

Is Jigsaw Sudoku harder than regular Sudoku?

Jigsaw Sudoku uses the same pure logic as classic Sudoku and requires no math, but most solvers find it slightly harder because the irregular regions break the box-scanning habits built up on rectangular grids. Candidates spread in less predictable ways, so you must follow the region outlines carefully and lean on techniques like the law of leftovers.

What is Mini Jigsaw Sudoku?

Mini Jigsaw is a 6x6 version of Jigsaw Sudoku using the digits 1 through 6. Six irregular regions of six cells each replace the rectangular boxes. Each row, column, and region must contain 1-6 exactly once. The smaller grid makes it an easy, low-pressure way to learn jigsaw-region logic before moving up to the full 9x9 puzzle.

Jigsaw Sudoku Rules: How to Play & Solve

Jigsaw Sudoku takes the familiar 9x9 grid and replaces the nine rectangular 3x3 boxes with nine irregular, contiguous regions that fit together like pieces of a jigsaw puzzle. The rules are otherwise identical to classic Sudoku: place the digits 1 through 9 so that every row, every column, and every region contains each digit exactly once. There is no arithmetic and no extra symbols — just pure logic, given a fresh twist by the unusual shapes. Jigsaw Sudoku is also known as Squiggly Sudoku, Geometry Sudoku, or Nonomino Sudoku.

What is Jigsaw Sudoku?

Jigsaw Sudoku is a logic puzzle played on the same 9x9 grid as standard Sudoku. The defining difference is the shape of the regions. In classic Sudoku, the grid is divided into nine neat 3x3 boxes. In Jigsaw Sudoku, those boxes are replaced by nine irregular regions — each made of nine connected cells, but bending and curving across the grid. Each region is outlined with a bold border so you can tell them apart.

Because the regions are irregular, they often span several rows and columns in ways the 3x3 box never does. This changes the flow of deductions. Some regions stretch tall and thin, others sprawl wide, and the interplay between region shape and the row/column rules is exactly what makes Jigsaw Sudoku interesting. A well-constructed Jigsaw puzzle has a single unique solution reachable through logic alone, with no guessing required.

Jigsaw Sudoku appeals to players who love classic Sudoku but want a new spatial challenge without learning arithmetic rules. It is a natural next step after Classic and Diagonal Sudoku.

Jigsaw Sudoku Rules

Jigsaw Sudoku has three fundamental rules. The first two are inherited from classic Sudoku, and the third replaces the box rule with the irregular-region rule.

Row rule: Each row of the 9x9 grid must contain the digits 1 through 9 exactly once. No digit may repeat in any row.
Column rule: Each column of the 9x9 grid must contain the digits 1 through 9 exactly once. No digit may repeat in any column.
Region rule: Each of the nine irregular regions must contain the digits 1 through 9 exactly once. No digit may repeat within a region, even though the region bends across multiple rows and columns.

Key idea: Everything you know about classic Sudoku still applies — you simply replace "3x3 box" with "irregular region" everywhere. The hard part is retraining your eye to scan along the jigsaw outlines instead of straight blocks.

The Law of Leftovers

The single most powerful technique unique to Jigsaw Sudoku is the law of leftovers (sometimes abbreviated LoL). It exploits the fact that both rows/columns and regions must each contain a complete set of the digits 1-9.

Consider a horizontal band — say the first two rows. Those two rows together must contain the digits 1-9 twice (each digit appears once per row). Now look at the irregular regions that overlap this band. Some regions sit entirely inside the two rows; others poke out, with cells above or below the band, while some cells of the band belong to regions that mostly sit elsewhere. The cells that "stick out" below the band and the cells inside the band that belong to outside regions must contain exactly the same multiset of digits. When the leftover area is just one or two cells, you can often pin them down to exact values.

Example: Suppose the top two rows are covered almost perfectly by two regions, except that one region dips one cell into row 3, and a single cell in row 2 belongs to a region centred lower down. By the law of leftovers, the digit in that protruding row-3 cell must equal the digit in the leftover row-2 cell. If you already know one of them, you instantly know the other.

Solving Strategies

Jigsaw Sudoku rewards a blend of classic techniques applied along irregular shapes plus a few region-specific tricks. Here are the core strategies, from fundamental to advanced.

1. Crosshatch along the regions

Pick a digit and scan the rows and columns that already contain it. For each region, the digit must go in the cells not eliminated by those lines. Because regions are irregular, a single placed digit can rule out surprising parts of a region — train yourself to trace the bold outline carefully.

2. Apply the law of leftovers

Look for bands of one, two, or three rows or columns where the overlapping regions almost line up. The smaller the leftover area, the more forcing the deduction. Corner regions and edge bands are the most productive places to start.

3. Hunt for hidden and naked singles

A naked single is a cell with only one remaining candidate; a hidden single is a digit that can go in only one cell within a row, column, or region. These appear constantly in Jigsaw puzzles, especially right after a law-of-leftovers deduction opens up the grid.

4. Use naked and hidden subsets

Naked pairs, naked triples, hidden pairs, and hidden triples work the same way they do in classic Sudoku, but remember to check them within regions as well as rows and columns. Irregular regions frequently create tidy subsets because their cells share unusual sets of lines.

5. Watch region-line interactions

When all candidates for a digit within a region are confined to a single row or column, that digit can be eliminated from the rest of that line outside the region (pointing). Conversely, when a digit in a line is confined to one region, eliminate it from the rest of that region (box-line reduction). These interactions are especially common in Jigsaw because regions overlap lines in varied ways.

Mini Jigsaw (6x6)

Mini Jigsaw applies the same idea to a compact 6x6 grid using the digits 1 through 6. Six irregular regions of six cells each replace the rectangular boxes. The rules are identical in spirit:

Each row must contain 1-6 exactly once.
Each column must contain 1-6 exactly once.
Each of the six irregular regions must contain 1-6 exactly once.

With only six digits, the law of leftovers resolves very quickly — comparing two rows against the regions covering them often forces values immediately. Mini Jigsaw is an excellent training ground: it teaches the same scanning habits and region awareness as the full puzzle, but a typical solve takes only a few minutes. In Sudoku - Brain Puzzles, Mini Jigsaw is free, so it is the perfect place to get comfortable before tackling the premium 9x9 Jigsaw.

Tips for Beginners

Trace the bold borders first. Before placing any digit, spend a moment following each region's outline so you can scan accurately. Mistaking a region's shape is the most common beginner error.
Start with the most constrained regions. Compact regions that hug a single corner or edge usually have the fewest options and are the best entry points.
Use pencil marks. Note all candidates in each cell. Digital apps like Sudoku - Brain Puzzles update pencil marks automatically as you place digits, which is a big help on irregular grids.
Learn the law of leftovers early. It is the technique that separates Jigsaw from classic Sudoku. Practise it on small bands until it becomes second nature.
Begin with Mini Jigsaw. The 6x6 grid teaches the same logic in a fraction of the time. Build confidence there, then graduate to 9x9.
Never guess. Every Jigsaw puzzle is solvable by logic. If you are stuck, re-scan the regions and look for a leftover deduction you missed.

Jigsaw Sudoku keeps everything you love about classic Sudoku — no math, pure logic, a single solution — while demanding a fresh way of seeing the grid. Master the law of leftovers and careful region scanning, and even tightly twisted puzzles will start to fall into place.

Jigsaw Sudoku Rules: A Complete Guide