Little Killer Sudoku is a Sudoku variant that adds diagonal sum clues around the outside of the grid. Small numbers with arrows indicate the sum of digits along a diagonal line, creating an extra layer of logic on top of standard Sudoku rules. It is one of the most popular competition-style variants and appears regularly in World Puzzle Federation contests.
What is Little Killer Sudoku?
A Little Killer Sudoku puzzle starts with a standard 9x9 Sudoku grid. Around the edges of the grid, you will see small numbers accompanied by diagonal arrows. Each number represents the sum of all the digits along the diagonal that the arrow points into. The diagonals run at 45-degree angles through the grid, and they can vary in length from a single cell up to nine cells for the main diagonals.
Unlike a regular Sudoku puzzle, a Little Killer grid typically starts with few or no given digits inside the grid itself. Instead, the external diagonal clues provide the information you need to deduce where each number belongs. All standard Sudoku rules still apply: every row, every column, and every 3x3 box must contain the digits 1 through 9 exactly once.
The name "Little Killer" comes from its relationship to Killer Sudoku. Both variants involve summing groups of cells, but they work quite differently in practice. Little Killer clues run along diagonals from outside the grid, whereas Killer Sudoku uses irregularly shaped cages inside the grid.
Rules of Little Killer Sudoku
Little Killer Sudoku follows all standard Sudoku rules plus one additional constraint:
- Standard rows: Each row must contain the digits 1 through 9 exactly once.
- Standard columns: Each column must contain the digits 1 through 9 exactly once.
- Standard boxes: Each 3x3 box must contain the digits 1 through 9 exactly once.
- Diagonal sum clues: Each number outside the grid indicates the sum of all digits along the diagonal that its arrow points to. The arrow shows both the direction and the starting corner of the diagonal.
One critical rule to understand: digits may repeat along a diagonal, as long as they do not violate the standard row, column, or box constraints. For example, a diagonal passing through three different rows, three different columns, and potentially different boxes could contain the digit 5 more than once.
How Little Killer Differs from Killer Sudoku
Players often confuse Little Killer and Killer Sudoku because both involve summing groups of cells. However, they are structurally different puzzles that require different solving approaches:
- Clue placement: Killer Sudoku clues appear inside the grid as dotted-line cages. Little Killer clues appear outside the grid with arrows pointing along diagonals.
- Cell grouping: Killer cages are groups of adjacent cells in any shape. Little Killer diagonals are straight lines running at 45-degree angles.
- Repetition: Killer cages forbid repeated digits within a cage. Little Killer diagonals allow repeated digits as long as standard Sudoku rules are not violated.
- Given digits: Killer Sudoku puzzles never have given digits inside the grid. Little Killer puzzles occasionally include a few givens, though many do not.
- Solving feel: Killer Sudoku solving relies heavily on combination mathematics within cages. Little Killer solving focuses more on intersection logic between diagonals and the standard constraints.
Solving Strategies for Little Killer Sudoku
Approaching a Little Killer puzzle requires combining standard Sudoku logic with diagonal sum analysis. Here are the most effective strategies, ordered from basic to advanced.
1. Start with short diagonals
Diagonals that pass through only one or two cells are the most restrictive. A single-cell diagonal directly tells you the value of that cell. A two-cell diagonal with a sum of 3, for instance, can only be 1+2 (in some order). Always resolve these first, as they give you free information.
2. Analyze extreme sums
A diagonal with a very low or very high sum constrains the possible digits. For example, a three-cell diagonal summing to 6 can only contain 1, 2, and 3 in some arrangement. Similarly, a three-cell diagonal summing to 24 must be 7, 8, and 9. Even when digits can repeat, extreme sums sharply limit possibilities.
3. Use the main diagonal sums
The two longest diagonals (corner to corner, nine cells each) have a maximum sum of 45 if they contained 1 through 9 once each. Since digits can repeat on Little Killer diagonals, the actual sum might differ. However, comparing the clue with 45 tells you whether the diagonal skews toward lower or higher digits overall, which narrows candidates across many cells at once.
4. Cross-reference diagonals with rows and columns
Each cell on a diagonal also belongs to a specific row, column, and box. If you know a row is missing only certain digits, and a diagonal passing through that row requires a certain sum contribution, you can often pinpoint the exact value. This intersection logic is the backbone of Little Killer solving.
5. Apply parity and modular arithmetic
Advanced solvers use parity (odd/even analysis) to narrow candidates. If a diagonal sum is odd and you know the parity of all but one cell on that diagonal, you can determine whether the remaining cell must be odd or even. This technique is especially powerful on longer diagonals where direct combination counting becomes impractical.
6. Look for overlapping diagonal constraints
Many cells sit at the intersection of two diagonals. When two diagonal clues share a cell, the constraints combine to limit that cell's value more than either clue alone. Identifying these intersection points early can accelerate your solve significantly.
Tips for Little Killer Sudoku
- Mark diagonal paths visually. Before solving, trace each arrow's diagonal across the grid so you know exactly which cells each clue refers to. Miscounting cells is a common early mistake.
- Remember that repetition is allowed. Do not automatically exclude a digit from a diagonal just because it already appears on that diagonal. Only row, column, and box rules prevent repetition.
- Use pencil marks generously. Little Killer puzzles benefit from thorough candidate notation. Write possible digits in each cell and update them as you apply diagonal constraints.
- Solve the corners and edges first. Corner cells belong to the shortest diagonals, a single row, a single column, and a single box. This concentration of constraints makes corners the easiest cells to resolve.
- Work multiple diagonals simultaneously. Rather than trying to complete one diagonal at a time, let information from several diagonals inform each other. A value determined by one diagonal often constrains cells on neighboring diagonals.
- Practice with smaller grids. If 9x9 Little Killer puzzles feel overwhelming, start with 6x6 or 4x4 versions to build intuition for how diagonal clues interact with standard rules.