Killer Sudoku
HardAbout hard killer sudoku
Hard killer sudoku starts you with 0 to 9 given digits. Most of the time it's closer to zero. You're solving almost entirely from cage constraints, and the cages go up to 5 cells.
This is where the 45 rule earns its reputation. Every row, column, and 3x3 box sums to 45. If you know the sum of all but one cage within a row or box, you can calculate the missing value directly. This technique bypasses candidate elimination entirely and gives you hard numbers.
You'll also lean on cage combination filtering more heavily. When a 4-cell cage has sum 15, there are 10 valid combinations. But once you place a digit in one cell, the remaining combinations for that cage shrink fast. Cross-reference cage combinations with row and column constraints, and the grid starts to break open.
Hard puzzles are solvable without guessing. If you feel stuck, check whether you've applied the 45 rule to every row and box. There's almost always a constraint you haven't used yet.