Hard sudoku

What makes a hard sudoku hard

Difficulty in sudoku is not really about how many numbers you are given, though these pages do give fewer as they get harder. It is about which techniques a puzzle forces you to use. An easy grid can be finished by scanning: look along a row, a column and a box, and one square will have only one candidate left.

Harder grids stop yielding to scanning alone. You start needing to hold candidates in mind across several squares at once, and to reason about where a number must go rather than what a square can take. That is the point at which most solvers start pencilling candidates in, which is why the on-screen version has pencil marks.

Every puzzle here has exactly one solution and can be reached without guessing. That is checked when the grid is dug rather than assumed: squares are removed only while the solution stays unique. A sudoku with two solutions is not a hard sudoku, it is a broken one, and it wastes the time of the person who trusted it.