Hard sudoku is a bookkeeping puzzle. You will mark candidates in every empty cell before you place your third digit, and most of the solve is pruning that map rather than filling cells — a naked pair here, a pointing set there, each one removing possibilities until something is finally forced. The pleasure is in the pruning, not the writing. If you find these frustrating rather than absorbing, the medium sheets are more likely to give you a good twenty minutes.
One hard 9x9 sudoku per page with cells sized deliberately generously, because full candidate marking needs room for up to nine small digits. Box divisions are printed heavily enough to stay visible under a grid full of pencil marks. Each puzzle has an answer page. Black and white on US Letter, one puzzle per sheet.
No. A well-formed sudoku has one solution reachable by logic. What changes with difficulty is how long the required chain of deductions is and how many techniques you need. If you are guessing, there is a deduction available that you have not spotted — most often a pointing pair or a hidden single in a busy box.
What is a pointing pair?
When all the candidates for a digit within one 3x3 box lie in a single row or column, that digit must go somewhere along that line inside the box — so it can be eliminated from the rest of that row or column outside the box. It is usually the technique that unlocks a stalled hard puzzle.
Should I mark candidates in pen or pencil?
Pencil, without exception. On a hard grid you will erase most of what you write, and a candidate map you cannot correct is worse than none. Some solvers use pencil for candidates and pen for confirmed digits, which makes the finished grid much easier to read.
How long is a hard sudoku meant to take?
Twenty-five to forty-five minutes is a fair range, and a good deal of that is the initial candidate marking. Speed is not really the point at this level — the puzzle is designed to reward accuracy, and one misplaced candidate can cost you the whole solve.