Sudoku - Puzzle

Sudoku (Japanese for "single number") is a popular logic-based, combinatorial number-placement puzzle. Despite using digits, Sudoku requires no math calculations—it is entirely a game of deduction, pattern recognition, and elimination. 1. Grid Structure & Layout The Main Grid: A classic Sudoku puzzle consists of a 9×9 grid, containing 81 individual cells (squares). Rows & Columns: The grid is structured into 9 horizontal rows and 9 vertical columns. Sub-grids (Boxes / Regions): The grid is further subdivided by bold borders into nine 3×3 sub-grids, often referred to as "boxes," "blocks," or "regions." 2. Objective & Core Rules The goal of the puzzle is to fill all 81 cells with digits from 1 to 9 such that every entry meets three simple conditions simultaneously: Row Rule: Each of the 9 horizontal rows must contain all digits from 1 to 9 without repetition. Column Rule: Each of the 9 vertical columns must contain all digits from 1 to 9 without repetition. Box Rule: Each of the nine 3×3 sub-grids must contain all digits from 1 to 9 without repetition. Key Rule: A well-constructed standard Sudoku puzzle has exactly one unique solution and can be solved using purely logical deduction without guessing. 3. How a Puzzle Starts Givens (Clues): At the start of the puzzle, a subset of the cells already contains pre-filled numbers. These are called "givens." Clue Count & Difficulty: Standard puzzles typically provide between 22 and 36 givens. The total number of clues doesn't automatically dictate difficulty; rather, the placement of the clues and the logical techniques required to find the next numbers determine how hard a puzzle is. Minimum Clues: Mathematically, a valid standard 9×9 Sudoku puzzle with a unique solution requires at least 17 givens. 4. Basic Solving Techniques Sole Candidate (Naked Single): When 8 numbers already exist in a row, column, or 3×3 box, the 9th empty cell can easily be filled with the only remaining missing number. Cross-Hatching (Scanning): Looking across adjacent parallel rows and columns within a 3×3 box to eliminate where a specific number cannot go, leaving only one valid spot. 5. Origin & Popularity History: The modern puzzle was designed in 1979 by Howard Garns (an American architect) under the name Number Place. It became immensely popular in Japan in 1984, where it was named Sudoku (short for Sūji wa dokushin ni karu, meaning "the digits must remain single"). It gained global popularity in late 2004 through newspaper syndication. Variants: Beyond standard 9×9, popular variants include Mini-Sudoku (4×4 or 6×6 for beginners), Killer Sudoku (adding arithmetic cages), Samurai Sudoku (5 overlapping 9×9 grids), and Hyper Sudoku (extra shaded regions).