Killer sudoku
Killer sudoku is a sudoku variant that starts with no given digits at all, and instead divides the grid into cages outlined with dotted lines, each labelled with the total that the digits inside it must add up to.
Every ordinary sudoku rule still applies — each row, column and three-by-three box holds 1 to 9 once each — and one rule is added: a digit may not repeat inside a cage. Together those constraints replace the givens entirely, which is why the grid can start empty and still have exactly one solution.
The technique that unlocks most grids is the rule of forty-five. Each row, column and box contains the digits 1 to 9 exactly once, so each sums to forty-five. If the cages sitting wholly inside a box add up to thirty-eight, the one remaining cell in that box must be a 7. The same subtraction works across pairs of rows and along the edges of boxes.
The rest is kakuro's arithmetic married to sudoku's placement: a three-cell cage totalling six can only be 1, 2 and 3, and a two-cell cage totalling seventeen can only be 8 and 9. The puzzle is also sold as sumdoku and, in Japan, as samunamupure.