Hard boards resisted our grader's first two technique tiers: solving them requires pair logic — naked pairs (two cells in a run locked to the same two candidates, which strips those digits from the rest of the run), hidden pairs, and sustained combination bookkeeping across several clues at once. Some also reward box-style arithmetic: summing a region's across clues against its down clues to pin an odd cell out.
Every hard board still has exactly one solution reachable by logic — that is verified mechanically before publication, so trial-and-error is never required, only deeper reading.
Pencil marks are essential here. If you are new to pair techniques, the combinations page explains them; the larger 9 × 9 and 9 × 11 boards are where they shine.