Killer sudoku combinations

The digits in a killer cage are all different and add up to the cage's sum, so the cage has to hold one of the combinations listed for its size and sum. A 2-cell cage of 10 is 1 and 9, 2 and 8, 3 and 7, or 4 and 6 — never two 5s.

Look for the one-way cages first. The highlighted rows can only be made one way: two cells adding up to 17 are always 8 and 9, and three cells adding up to 7 are always 1, 2 and 4. Those cages are the way into most killer puzzles.

Then cross out what the grid rules out. Three cells adding up to 8 are 1 2 5 or 1 3 4. If the cage shares a row with a 5, it can't be 1 2 5, so it is 1, 3 and 4 — and either way it holds a 1. That is what the digit buttons in the calculator do.

Big cages read better from the other end. Every row, column and box adds up to 45, so a cage of eight cells is the digits 1 to 9 minus whichever one makes up the difference.