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A nonogram is a grid where the numbers beside each row and column tell you which cells to fill, and the filled cells form a picture. You solve it with a handful of line-by-line techniques, no guessing required. Here are the rules, every core technique with a concrete example, and a full 5x5 puzzle solved from start to finish.

Killer sudoku is classic sudoku plus cages: dotted groups of cells whose digits must add up to the small number in the corner, with no digit repeated inside a cage. You solve it with two tools on top of ordinary sudoku logic: knowing which digit sets can make each sum, and the rule that every row, column and box adds up to 45.

Most sudoku puzzles, up to and including many labelled expert, can be solved with about a dozen techniques. Learn them in order: scanning and singles finish easy puzzles, subsets and pointing pairs carry you through hard ones, and X-Wing, Swordfish and XY-Wing unlock the toughest. Here is each one, how to spot it, and when to reach for it.

A sudoku variant keeps the classic rules and adds one constraint: a diagonal, extra windows, irregular regions or cage sums. Each extra rule gives you new places to find singles and eliminations, so variants are often no harder than classic sudoku once you know where to look. Here are eight popular variants, what each one adds, and a tip that makes it click.