Clues must rule out every competing grid
A Sudoku clue does more than fill a square: it helps distinguish the intended completed grid from other grids that obey the same rules. A puzzle has a unique solution only when no alternative completion satisfies every given number.
Some groups of cells in a completed Sudoku can be changed together to make a different valid grid. Such a group is often called an unavoidable set: if a puzzle leaves every cell in that group blank, the alternate grid may remain possible. To guarantee uniqueness, the clues must block every such route to a second solution.
Why 16 clues cannot be enough
There is no simple rule that says a particular square needs a clue, or that every puzzle needs one clue in each row or box. The challenge is that the clues’ positions interact: a clue that rules out one alternative may do nothing to rule out another.
The 17-clue minimum was established by exhaustive computation. In effect, computers checked the possible ways a 16-clue puzzle could be arranged and showed that none can block all competing completions. This is a mathematical result about the full set of possible arrangements, not just a search that failed to find a 16-clue example.
Seventeen is a floor, not a recipe. A carefully placed set of 17 clues can determine one grid, but adding 17 numbers anywhere does not guarantee a unique answer. What matters is not only how many clues there are, but which alternative solutions their positions eliminate.
