Killer Sudoku Tips: Cage Sums, the 45 Rule and Unique Combinations
By the CrazyArcade team ·
Killer Sudoku keeps the normal Sudoku rules, where each row, column and 3x3 box holds the digits 1 to 9 once, and adds cages: groups of cells outlined with a sum in the corner. The digits in a cage must add up to that sum, and a digit cannot repeat inside a cage. Hard killer puzzles often start with no digits at all, so the sums are your only clues.
We use our own Killer Sudoku for the examples. If you are new to Sudoku itself, our guide to Sudoku techniques covers the basic scanning methods, which all still apply here.
Learn the unique combinations
Some sums can only be made one way. A two-cell cage of 3 must be 1 and 2, and a two-cell cage of 17 must be 8 and 9. A three-cell cage of 6 is always 1, 2 and 3, and a three-cell cage of 24 is always 7, 8 and 9. A four-cell cage of 10 is 1, 2, 3 and 4, and a four-cell cage of 30 is 6, 7, 8 and 9.
When you see one of these cages, write the digits as pencil marks right away. They often settle a whole row or box.
The 45 rule
Every row, column and 3x3 box adds up to 45, because 1 + 2 + ... + 9 = 45. If the cages inside a box cover all its cells except one, add up those cage sums and subtract from 45: the result is the missing cell. If one cage sticks out of the box by a single cell, the same subtraction tells you the value of that outside cell.
The rule also works across two or three rows or columns together, which add up to 90 or 135. Look for places where cages almost line up with a row, column or box edge.
Combine cages with normal Sudoku
Once you have pencil marks from cage combinations, the usual Sudoku techniques take over. If a cage of 1, 2 and 3 sits in one row of a box, no other cell in that row can hold those digits. Each placed digit also narrows the options for the cages around it, so keep switching between cage logic and row, column and box logic.
Start small
Begin with an Easy puzzle, which gives you some starting digits, and get used to reading the cage sums. Move to Hard, with no starting digits, once the unique combinations and the 45 rule feel natural. Our Killer Sudoku shows the possible combinations for the selected cage, which helps while you learn them.