Sudoku Online Generator

Purpose & User Intent: This tool solves the problem of quickly generating valid Sudoku puzzles with controllable size and difficulty, along with their solutions. It targets puzzle enthusiasts, educators, and developers integrating puzzles into worksheets or apps. When a reproducible puzzle is needed for class activities, self-practice, or testing, this generator provides a ready-to-use puzzle and solution set.
Core Logic & Features: Required features include complete grid generation via backtracking, a removal step that preserves a unique solution, support for 4x4 and 9x9 grids, adjustable difficulty presets, and optional seed-based reproducibility. Outputs include puzzle and solution representations, with an export option for printing or integration. Optional/advanced features include batch generation, JSON export, and printable formatting.
Inputs & Outputs: Inputs include grid_size (4x4 or 9x9), difficulty (easy/medium/hard), seed (optional integer), and an option to generate the solution. Outputs deliver puzzle_grid and solution_grid in structured formats (2D arrays or textual grids) where puzzles display blanks for clues and solutions show all digits.
Algorithms & Calculations: Utilizes a backtracking algorithm to build a complete Sudoku solution, followed by a clue-removal phase that maintains a unique solvable puzzle. If a seed is provided, the pseudo-random sequence is deterministic to ensure reproducibility. The solver verifies that the resulting puzzle has exactly one solution before presentation. Error & Edge Cases: Handles invalid grid_size values, unsupported grid sizes, and seeds that necessitate retries. If removal produces non-unique solutions, the algorithm retries with alternate clue removal. External data unavailability is treated as generation retry only; no user-facing UI messaging is described here. Industry/Region & Localization: Grid sizes align with standard Sudoku practice (4x4, 9x9). Rules and terminology are locale-agnostic; no currency or region-specific formats are assumed. Assumptions & Exclusions: Assumes the requested sizes are 4x4 or 9x9 unless extended. Excludes UI interactions, styling, and accessibility considerations; focuses strictly on domain logic, inputs/outputs, and reproducibility mechanics.