It is always possible to solve sudoku puzzles. Most are designed for humans to be able to solve using logic, deduction and learned techniques. They are typically in the range of easy, medium, hard and expert (or similar terms).
There are puzzles that are nearly impossible for a human to solve but they are the exception and there aren’t very many of them. One that is very difficult is called Sudoku AI Escargot.
A “well-formed” sudoku puzzle is one that only has one solution. The vast majority of puzzles available are well-formed. It is possible to find puzzles that are not well-formed but they are mistakes or not designed well. Sudoku puzzles available to solve imply that they are well-formed.
Myth 7 Sudoku came from Japan > >
Sudoku - the puzzle that addicts