We know from this paper that there does not exist a puzzle that can be solved starting with 16 or fewer clues, but it implies that there does exist a puzzle that can be solved from 17 clues. Can all valid sudoku puzzles be specified in 17 clues? If not, what is the minimum number of clues that can completely specify every valid puzzle? More formally, does there exist a valid sudoku puzzle (or, I guess it would be a set of puzzles) that cannot be uniquely solved from only 17 clues? If so, then what is the minimum number of clues, $C$, such that every valid sudoku puzzle can be uniquely specified in $C$ or fewer clues?
Minimum number of clues to fully specify any sudoku?
sudoku;combinatorics