Killer sudoku

Killer sudoku (sometimes called sum sudoku) takes ordinary sudoku and adds addition. The grid starts with no given digits at all, instead you get dotted regions called cages, each with a small target sum printed in its top-left corner. Everything has to be deduced from those sums plus the normal sudoku constraints, which is why it trains arithmetic and logic at the same time and has become one of the most popular sudoku variants.

• Each row, column and 3×3 box contains the digits 1–9 exactly once (as in normal sudoku).
• The digits inside a dotted cage must add up to the number printed in its corner.
• No digit may repeat inside a single cage.

Your best weapon is the rule of 45. The digits 1–9 add up to 45, so every row, every column and every 3×3 box must total exactly 45. Add up the cages that sit almost entirely inside one box, subtract from 45, and the single cell sticking out is determined by arithmetic alone.

After that, start from the cages with the fewest possible combinations. A two-cell cage summing to 3 can only be 1+2; summing to 17 it can only be 8+9. A three-cell cage summing to 6 must be 1+2+3, and 24 must be 7+8+9. Anchor yourself on those extreme sums, pencil the candidates in with the notes button, and the grid opens up from the corners inward.

For classic grids, head to the 20 free daily sudoku puzzles. To brush up on the fundamentals, read how to play sudoku, and if a grid defeats you, the sudoku solver is there to check it.