foo123/sudoku.js ? reverse-engineered prompt

Build me a simple Sudoku app in pure JavaScript that lets a user play, generate, and solve Sudoku puzzles in the browser.

I want it to feel fast and lightweight, with a clean interface where I can click into cells, enter numbers, clear mistakes, and check whether the puzzle is valid. It should also be able to create new puzzles and solve an existing board automatically. If it helps, include a small demo page so I can open it and use it right away without any setup.

Keep the code easy to read and organize it so the game logic, puzzle generation, and solving are separated cleanly. Use plain JavaScript and make sure it runs in a normal browser. If you need to look up any current browser details or best practices while building it, go ahead and do that.