Hard Sudoku

Where eliminations begin

A puzzle is only accepted as Hard if the solver needs one or two elimination steps to finish it, and no advanced pattern at all. It starts with 30 to 34 givens.

That single elimination is the wall players hit. You scan the grid, find no forced digit anywhere, and conclude the puzzle is broken. It is not — the next move is not a placement, it is a deduction about candidates.

The three patterns that unlock this level

• Naked pair: two cells in one unit hold the same two candidates, so those digits belong to that pair and can be erased everywhere else in the unit.
• Pointing pair: inside a box, all remaining spots for a digit sit on one row or column, so the digit can be removed from the rest of that line.
• Box/line reduction: the mirror image — a digit in a row or column can only appear inside one box, so it disappears from the rest of the box.

Pencil marks stop being optional

You cannot see a naked pair without candidates written down. On Hard, fill notes for the units you are working in and keep them updated as you place digits — an out-of-date pencil mark is worse than none.

If you use a hint here, read the explanation rather than taking the digit. The hint names the technique and shows the cells that justify it, which is the part that carries over to the next puzzle.

How long it should take

Expect a Hard grid to stall at least once. The stall is the puzzle working as designed: it is asking for an elimination, not a faster scan. Once the elimination lands, the rest usually falls quickly.