If a Sudoku has one and only one solution, then it is always solvable without guessing or backtracking. It just might not be within the scope of the human brai

If a Sudoku has one and only one solution, then it is always solvable without guessing or backtracking. It just might not be within the scope of the human brain. There exist (many) configurations where every cell is influenced by every other, so to solve any one cell essentially requires a simultaneous solve of the entire puzzle. There's no theoretical reason a human couldn't do that too; it's a problem simply of computational capacity not fundamental approach.