Every Killer Sudoku cage publishes a sum clue equal to the total of digits placed inside that cage. Unlike Killer's cousins in puzzle magazines that sometimes specify operations, classic Killer Sudoku always uses pure addition across orthogonally connected cells. Understanding sums means mastering partitions—lists of distinct digits adding to the clue while respecting Sudoku constraints wrapping the cage.
Notation and reading order
Publishers usually print sums near the cage's top-left cell or along the smallest-numbered cell within the cage footprint. When puzzles omit printed borders on screens, digital interfaces mimic bold outlines; always verify software legends before assuming clue placement.
Partitions and feasibility
Feasible partitions shrink as cage size grows because digits must stay distinct inside the cage and coexist with Sudoku lines. A six-cell cage totaling 20 admits fewer compositions than intuition guesses.
Automated combination tables help beginners internalize boundaries until mental arithmetic suffices.
Parity and modular filtering
Even sums with odd cage counts force odd digit multiplicity constraints; parity filters discard half of speculative tuples instantly.
Likewise, modulo-3 reasoning occasionally collapses triples when totals interact with known residues along rows.
Interaction with Sudoku houses
Sums never override Sudoku—they refine candidates inside cages until uniqueness emerges. When cage totals align perfectly with row deficits, solvers derive pseudo-givens faster than scanning alone allows.
Overlapping cage arithmetic
Adjacent cages exchange information through shared rows: eliminating {4,5} from one cage often trims tuples from neighbor cages intersecting that row.
Sanity checks before guessing
Sum mismatches usually indicate transcription slips rather than flawed publishers—re-sum clusters before doubting uniqueness.
Further reading
Continue with understanding cage combinations and sum elimination techniques.