Here you have some possibilities, you can get simple-sudoku to generate a puzzle for you, there are 5 difficulty ratings to choose between, all these puzzles are solveable, and have only one solution.
The "Solution" tab generates a Sudoku Puzzle based on the solution generated ... The logic for removing elements is relatively simple, and therefore only "Easy" to "Easy / Medium" puzzles can be ...
Pencil is, of course, easy to erase in a hurry once you find the solution—or realize you made a mistake. Your pencil won't ...