How to play Killer Sudoku

The familiar Sudoku constraints still govern the whole board: each digit from 1 to 9 appears once in every row, column, and bold 3×3 box. Killer Sudoku may begin without printed givens, but the row, column, and box rules are active from the first move. A cage outline adds another region whose small corner number is the required sum.

Digits cannot repeat inside a cage, even when its cells lie in different rows, columns, or boxes. A two-cell cage totaling 4 can therefore contain 1 and 3, but not 2 and 2. The cells do not have a required order, so a combination narrows possibilities before it identifies exact positions.

Small or extreme totals usually have the fewest combinations. A two-cell cage totaling 3 must use 1 and 2, while a two-cell cage totaling 17 must use 8 and 9. A three-cell cage totaling 6 must use 1, 2, and 3. These facts reserve digits for a cage, but row and column evidence is still needed to decide their order.

Do not list arrangements as separate combinations. For a 10 cage, 1 plus 9 and 9 plus 1 describe the same pair. First identify the unordered set, then use crossings with existing candidates and neighboring cages. Removing impossible sets is often enough to create a single candidate in one cell or one location for a digit in a region.

Every complete Sudoku row, column, and 3×3 box contains 1 through 9, which add to 45. If cages fit exactly inside one region, their totals must add to 45. More often, one cage crosses the boundary. Subtract the totals fully inside the region to calculate the value of the cells that protrude into or out of it.

Draw the boundary in your mind before subtracting. Count only the cage cells on the relevant side, and make sure every other cell in the row, column, or box is accounted for. The 45 rule produces a sum constraint, not automatically an ordered answer; ordinary candidates may still be required to place the resulting digits.

Cell notes show digits allowed by the cell's row, column, box, and cage. Cage combinations describe sets of digits that can satisfy the total across several cells. Keep both ideas clear: removing one combination can change several cell candidates, while placing one digit can invalidate every combination that does not contain it.

Update nearby notes after every placement. Remove the digit from its row, column, box, and the rest of its cage, then recompute any cage whose available cells changed. A candidate is permission, not proof. Two possible digits in a cell remain unresolved until another constraint removes one or reserves it elsewhere.

A common mistake is choosing numbers that reach the total while ignoring a repeated cage digit or a conflict in the crossing row, column, or box. Check all constraints before entering a value. Another mistake is forcing one attractive combination when several distinct-digit sets still satisfy the sum.

When progress slows, scan the whole grid instead of guessing inside the cage you were studying. Look for extreme totals, cages confined to one region, ordinary Sudoku singles, and boundaries where the 45 rule applies. Clever Pause's published grids have one verified solution and a supported logical trace, so a defensible next deduction exists.