Solving hard classic sudoku

Hard classic sudoku is the first tier where pencil marks stop being optional. The new techniques — hidden pairs and triples, naked triples, pointing pairs that fire across multiple boxes — all rely on noticing patterns in candidate sets that aren't visible to the naked eye. Most solvers feel the difficulty jump from medium to hard more than any other transition on the ladder. The cause is structural: every technique below hard could be spotted with discipline and careful scanning. Hard requires notation as working memory.

Pencil marks as working memory

Most hard puzzles need full pencil marks across most empty cells before the techniques can fire. The discipline is to fill in candidate notes for every cell that hasn't resolved after the first scanning pass — not just the cells that look interesting. The techniques at this tier work by reading patterns across multiple cells, and a missing pencil mark is a missing piece of the pattern. Our piece on reading pencil marks like a shape covers the visual habit that turns the busy grid back into something readable.

The new techniques hard introduces

Naked triples are the three-cell version of the naked pair. Three cells in the same unit whose combined pencil marks contain only three distinct digits — the digits 2, 5, and 8, say — must contain those digits in some order, eliminating 2, 5, and 8 from every other cell in the unit. The cells don't have to each contain all three candidates; one cell might have only 2 and 5, another only 5 and 8, the third 2 and 8. As long as the three cells collectively use only three distinct digits, the elimination fires.

Hidden triples are the same logic flipped. Three digits whose only possible positions in a unit are confined to three cells — those three cells must contain those three digits in some order, and any other candidates in those cells are eliminated. Hidden triples are harder to spot than naked triples because the pattern isn't visually clustered; you have to track three digits across three cells rather than three cells with the same candidate set. The deep-dive on naked and hidden pairs and triples walks through the recognition pattern for both.

Hidden pairs appeared at medium but become much more frequent at hard. The pattern is the same — two digits whose only positions in a unit are two specific cells — but at hard the pair often hides in noisier candidate sets, with extra digits in both cells that don't belong to the pair. Spotting the hidden pair requires actively scanning a unit by digit, not by cell.

Pointing pairs and claiming, in earnest

Locked candidates — pointing pairs and claiming pairs — appeared at medium but at hard they're the move that breaks most stalls. The pattern: a digit's only possible positions inside a box all sit in one row or column, so the digit can be eliminated from that row or column outside the box (pointing). Or the reverse: a digit's only positions in a row or column all sit inside one box, so the digit can be eliminated from the rest of that box (claiming). Our piece on pointing pairs and the snake covers both. At hard, every puzzle has at least one pointing or claiming move, and many have several.

When hard stalls

Hard stalls in two characteristic ways.

Incomplete pencil marks. The most common stall at hard isn't a missing technique — it's a missing pencil mark. A cell that wasn't fully noted has the digit you need, but you can't see it because the candidate set isn't on the page. The fix is mechanical: when you stall for more than three or four minutes, do a full pencil-mark audit. Walk every empty cell and verify its candidates against the row, column, and box. The audit takes two minutes; the move is almost always already there once the notation catches up.

Pattern-blindness on hidden subsets. Hidden pairs and triples are the techniques most solvers underuse. Naked subsets are visually obvious — three cells all carrying the same small candidate set — but hidden subsets ask you to scan by digit, looking for digits whose positions are confined. When a hard puzzle stalls and the audit doesn't surface a missed pencil mark, the next move is often a hidden subset. Walking every unit by digit (which digits appear in only two or three cells of this unit?) reveals them.

Two habits to drop

Skipping the pencil-mark pass. The instinct to push forward at the start of a hard puzzle, placing a few easy singles before getting around to notation, is fine. But once the singles run out, full pencil-marks need to happen before any further hunting. Solvers who try to spot pairs and pointing pairs without notation either miss them or guess.

Hunting for techniques out of order. Hard rewards a routine — full pencil-marks, then check for naked pairs and triples, then locked candidates, then hidden subsets. Solvers who jump straight to the most exotic technique they know often miss the simpler move that was already there. The piece on which technique is this puzzle asking for covers the routine in more depth.

When pencil marks become a habit you don't think about and the named techniques start firing on first sight, you're ready for expert, where X-wings and swordfish enter the rotation. Hard is the tier most regular solvers settle at for the longest stretch — months, sometimes years — and that's correct pacing. The techniques here are the foundation everything above is built on.