What is the minimum number of clues a Sudoku can have?

In 2012, Gary McGuire, Bastian Tugemann, and Gilles Civario at University College Dublin published a proof that no valid 16-clue Sudoku exists. Their work was primarily computational: they searched the full space of possible 16-clue grids and verified that none produced a unique solution. The search required approximately 7 million core-hours of computation.

Prior to this, it was widely believed that 17 was the minimum and thousands of 17-clue puzzles had been found experimentally. McGuire's team provided the first rigorous proof that 16 is impossible.

17-clue puzzles are extremely sparse - 17 given digits in 81 cells, leaving 64 empty. They are among the hardest puzzles to solve and typically require advanced techniques. Finding valid 17-clue puzzles itself required decades of computational effort. As of the time of writing, over 49,000 essentially different 17-clue Sudoku puzzles are known.

Published puzzles aimed at human solvers rarely go below 22 clues. Expert and Master difficulty puzzles typically use 22-27 given digits, while Easy puzzles use 36-45. The 17-clue minimum is a theoretical bound - In practice, solvability with good technique and an enjoyable solving path matter far more than clue count alone.