Advanced Killer Sudoku rules
Killer Sudoku is classic Sudoku plus cages. This page is the longer strategy guide: the combinations that actually get used, how a cage talks to a row or a box, and how to stay on logic when the grid looks full of options.
The rules that never change
Every row, every column and every 3×3 box contains the digits 1 to 9 exactly once. A cage is a dashed group of cells with a small total in the corner. The digits inside that cage add up to the total, and no digit repeats inside the cage.
A one-cell cage is a given: the total is the digit. A two-cell cage is the workhorse of most grids. Larger cages are usually solved by what they cannot be, not by listing every split of the total.
Cage combinations worth memorising
Two cells totalling 3 can only be 1 and 2. Totalling 4 is 1 and 3. Totalling 17 is 8 and 9. Totalling 16 is 7 and 9. The same idea runs up the middle: 10 can be several pairs, so it is a weak cage until a row or box removes some of them. Write only the pairs that survive, not every pair that adds up.
Three cells totalling 6 are 1, 2 and 3 in some order. Totalling 7 is 1, 2 and 4. Totalling 24 is 7, 8 and 9. A cage of 23 is 6, 8 and 9. When a cage is this extreme, the digits are fixed as a set even though the order is not. Place the set, then let the houses decide the order.
The 45 rule, innies and outies
Digits 1 through 9 add up to 45. Any row, column or box therefore sums to 45. If cages cover a whole house plus one extra cell, that extra cell (an outie) is the cages’ total minus 45. If cages leave one cell of the house uncovered (an innie), that cell is 45 minus the cages you can already see.
The same arithmetic works on two boxes at once, or on a row plus a cage that spills into the next row. You do not need a new rule for each shape. Add the cages you trust, subtract 45 once per complete house, and the remainder is the cell or cells that stick out.
Cages that cross a box
A cage that sits in two boxes is more useful than a cage that sits inside one. The digits it uses are forbidden in both boxes only for the cells it occupies, but its sum still has to be possible with the digits each box has left. If one box can only contribute a 9, the rest of the cage is the total minus 9, split across the other cells.
When two cages together cover a box except one cell, that last cell is an innie of the box. Mark it as soon as you see it. Players who wait until the box is almost full usually discover the same digit ten minutes later.
What to do when several digits still fit
Do not try the first pair that adds up. Delete pairs that repeat a digit already used in the same row, column or box, and pairs that would force a repeat inside the cage. If only one pair remains, those two cells are a naked pair: no other cell in that house may use either digit.
If a digit can sit in only one cell of a cage once the houses are considered, place it. If a digit of the cage can sit in only one cell of a row, place it even if the cage still has other free cells. The cage and the house are the same constraint seen from two sides.
Hard and expert grids
Hard puzzles rarely give you a one-cell cage near the start. Expect to run the 45 rule on a band of three boxes, then a single row, before any digit is written. Expert puzzles add longer cages whose combinations only collapse after two houses have been reduced. The logic is the same; the chain is longer.
Guessing is what you do when a combination was eliminated too early. If the grid contradicts itself, undo to the last cage whose pair list you shortened and put the deleted pair back. A unique solution never requires a lucky trial if the combination list is complete.