Killer Sudoku

1.Killer Sudoku is a popular variation of the classic Sudoku puzzle that combines standard Sudoku rules with an additional layer of complexity involving cages. In Killer Sudoku, numbers within outlined regions, called "cages," must sum to a specified value, and numbers cannot repeat within these cages or in rows, columns, and 3x3 subgrids. Standard Sudoku Rules Apply: Numbers 1-9 must appear exactly once in each row, column, and 3x3 subgrid. Cages and Sums: The grid is divided into "cages" (outlined regions), each with a target sum indicated in its top-left corner. The numbers within a cage must add up to that sum, and no number can be repeated within a single cage. Solving Techniques: Killer Sudoku often involves techniques beyond basic Sudoku, including mental arithmetic and logical deduction related to cage sums and number exclusions. The "45 rule" is a common technique, based on the sum of numbers 1-9 being 45. Origins: Killer Sudoku was established in Japan by the mid-1990s as "samunamupure," a Nipponized form of "sum number place," and introduced to the English-speaking world by The Times in 2005. Difficulty: While the name suggests a challenging puzzle, simpler Killer Sudokus can be easier than regular Sudokus, and the difficulty can vary significantly, with hard versions requiring considerable time and mental effort.