Killer Sudoku is played on the standard 9×9 Sudoku grid divided into nine 3×3 boxes. Before considering cages, every rule from classic Sudoku applies: each horizontal row must contain digits 1 through 9 exactly once, each vertical column likewise, and each 3×3 box likewise. These constraints are non-negotiable; cages never relax them.
What is a cage?
A cage is a set of orthogonally adjacent cells—think polyomino shapes—that bond together visually with thick outlines. Each cage displays a small sum clue (often top-left of the cage) describing the total obtained by adding every digit placed inside that cage. Cells belong to exactly one cage; cages partition the grid completely.
Sizes vary from single-cell cages—functionally fixed digits printed as givens—to sprawling regions containing eight or nine cells on extreme puzzles. Larger cages demand heavier combination reasoning.
The no-repeat rule inside cages
Digits inside a cage cannot repeat, even if classic Sudoku rules would permit duplicates across distant units. That stipulation dramatically shrinks candidate sets for cage totals that would otherwise admit duplicate pairs.
Example: a two-cell cage summing to 10 cannot use {5,5}; it must use {1,9}, {2,8}, {3,7}, or {4,6}. Sudoku lines crossing those cells further prune the menu.
How sums interact with Sudoku houses
Every digit placement must simultaneously respect row uniqueness, column uniqueness, box uniqueness, and cage totals. Sometimes arithmetic alone leaves multiple tuples alive; Sudoku constraints kill all but one. Conversely, Sudoku might leave two candidates until cage parity decides.
Advanced puzzles exploit intersections where cage footprints wrap around nearly solved rows. Early solvers should trace cage borders carefully whenever two candidate tuples appear symmetric—geometry often breaks ties.
Uniqueness and well-posed puzzles
Published Killer Sudoku puzzles assume exactly one solution consistent with all clues. Unlike casual brainstorming, competitive solving trusts uniqueness so solvers can eliminate branches that produce alternate completions—even when short-term arithmetic seems ambiguous.
Home constructors should verify uniqueness computationally; guessing forward without confirmation risks flawed grids.
Optional variants you might encounter
Some publishers tint cages or color partitions differently while preserving rule semantics. Killer variants mixing diagonal constraints or extra regions layer atop these fundamentals—master vanilla Killer before chasing hybrids.
Practice checklist
Before attacking diabolical magazines, rehearse: can you articulate why each cage tuple survives elimination? Can you spot immediate cage singles analogous to Sudoku singles? Reinforce with cage combinations and hands-on play via easy practice grids.