Sudoku-YFoundations
Killer Sudoku: cages and sums
Killer adds sums to the familiar Sudoku constraints. A cage can tell you which digits belong together without telling you their order. Keep these two deductions separate.
Practise on a board ↓LOOK · TRY · UNDERSTAND
Try it and see why
The digits, but which order?
Cage A1/A2 totals 10. The shown notes are complete, with no repeated digit in the cage.
Our own partial teaching board, not a full puzzle. Large digits are placed values; small digits are candidates. Dots mean the cell is not described here. Complete candidate lists are part of the stated scenario, not calculated from the dots.
Green outline = evidence · Purple “try” = an assumption · Crossed out = removed candidate
The cage uses 4, 6. Does that prove A1=4?
See the reasoning
Both 4+6 and 6+4 total 10. You need another constraint to choose their order. Try both arrangements above.
Digit set 1/9 · A different digit set in the same pattern, not a new full puzzle.
Read the source principles: Sudoku.com — Killer rules
Read the cage boundaries
On a 9×9 board, rows, columns and 3×3 boxes still contain 1–9 without repeats. A dotted cage groups cells whose values add to its small corner total. Digits cannot repeat within a cage, even when it crosses box boundaries.
A box and a cage are different regions. A placement must satisfy both.
Sudoku.com — Killer Sudoku rules · SudokuWiki — Killer Sudoku solver
A worked combination example
Original teaching scenario: a two-cell cage A1/A2 totals 10. Its combinations are {1,9}, {2,8}, {3,7} and {4,6}. The pair {5,5} repeats a digit and is invalid. Suppose column and box constraints leave A1 with {1,4} and A2 with {6,8}. Checking each sum leaves only A1=4 and A2=6.
If both cells instead allow {4,6}, you know the combination but not the order. Look for another constraint before entering a final value. This partial scenario is not a complete puzzle.
Use 45 only with exact coverage
The values 1–9 sum to 45, so each row, column and box on a 9×9 grid has that total. Subtract totals of cages fully inside the region only when coverage is exact, without gaps or double counting.
Sudoku.com — Killer Sudoku rules
Try before revealing
Cages entirely inside row A cover eight cells and total 38. Only A9 remains. What is A9?
Show explanation
A9=45−38=7. The 38 must cover exactly the other eight cells in that row. A cage crossing the row boundary cannot simply have its whole total subtracted. This is a teaching condition, not a complete grid.
Try it in Sudoku-Y
Return to the game and choose Killer and a size. Sudoku-Y cages can include starting clues. Hints cover single candidates and the last missing cell in a cage; direct answer reveals are labeled. The advanced technique finder remains in Classic 9×9.
The region total changes with size: 1–4 totals 10, 1–6 totals 21, and 1–16 totals 136. Do not carry the number 45 into every variant.
References and further reading
Read the source explanations and compare them with our examples. Links are references, not endorsements or claims of affiliation.