Solving medium classic sudoku

Medium classic sudoku is the tier where the puzzle starts asking you to look at two regions at the same time. Easy gave you naked singles and hidden singles — eight digits ruled out by one region's worth of context, or one digit's only home inside one region. Medium asks for the next step: a pair of cells that share the same two candidates, eliminating those candidates from the rest of their unit. A digit confined to one row of a box, eliminating it from the same row in two other boxes. Most of the techniques are extensions of what easy already taught you — but the way you apply them changes.

Pencil marks become useful

At easy, pencil marks were optional. At medium, they're how you spot most of what's there. The new techniques work by noticing that two cells share a candidate set, or that a digit's possible positions inside a region are confined to one row — and you can't see either pattern reliably without notation. Most solvers don't pencil-mark the entire grid the way they will at hard; they pencil-mark the cells that haven't resolved after the first scanning pass. Our piece on pencil marks without the clutter covers the lightweight notation style that works at this tier.

The new techniques medium introduces

A naked pair is two cells in the same unit (row, column, or box) whose pencil marks contain only the same two digits. If two cells in box 3 can each only hold a 4 or a 7, the 4 and the 7 in that box must be in those two cells — so 4 and 7 can be eliminated from every other cell in box 3. The deep-dive on naked and hidden pairs and triples covers the mechanics in detail. At medium, naked pairs are the workhorse. They appear in most puzzles and they often unlock the next single.

Locked candidates — sometimes called pointing pairs or claiming pairs — are the other new move. If a digit's only possible positions inside a box all sit in the same row, that digit must end up in one of those cells, which means it can be eliminated from the rest of that row outside the box. The reverse also fires: if a digit's only positions in a row all sit inside one box, it can be eliminated from the rest of that box. Our piece on pointing pairs and the snake walks through the recognition pattern.

Hidden pairs appear less often at medium and more often at hard, but they show up in roughly half of medium puzzles. The pattern: two cells in a unit are the only places where two specific digits can go. The cells might have other candidates — extra noise — but those other candidates are eliminated, because the pair has to occupy those two cells. Hidden pairs require pencil marks to spot reliably; they're the technique that justifies the notation overhead.

The shift in scanning

Easy rewarded scanning one digit at a time across each box. Medium rewards scanning by unit — looking at one row or column or box and asking what its full candidate landscape looks like, not just where one digit can go. The piece on scanning cells to scanning units covers the mental shift. The short version: instead of "where can the 6 go," ask "what does this row need, and where can each missing digit go." That framing surfaces pairs and locked candidates the digit-by-digit scan misses.

When medium stalls

Medium stalls in two characteristic ways.

Single-region thinking. Most easy stalls broke when you scanned a different region — same kind of move, different place. Medium stalls usually require thinking across two regions at the same time. A digit's positions inside a box matter only because they line up with a row or column outside the box; a pair only fires because the cells are in the same unit. When a medium puzzle stalls, the move you're missing is almost always one that combines information from two regions. The fix is to walk every row, then every column, then every box, and at each step ask what's true that involves more than just that region.

Under-noting. The other failure mode is skipping pencil marks where they were actually needed. A typical pattern: you've placed half the grid using easy-style scans, the next single isn't visible, and you push forward without writing notes. The notes would have shown a naked pair in box 4 that you couldn't see by inspection. Two minutes of pencil-marking the unresolved cells usually surfaces the move that's been there since the puzzle stalled.

Two habits to drop

Treating medium like easy. Some solvers carry the easy-tier instinct ("the next move is always just there") into medium, and stall when the obvious moves run out. Medium is meant to feel different — pause, write, look. Embracing the slowdown is the move that gets you through medium consistently.

Bashing forward without looking up. When you've placed three or four digits in a row and built momentum, it's tempting to keep scanning the same regions you just changed. But after several placements the moves available elsewhere on the grid have shifted too — a hidden pair on the other side of the grid has become spottable, a pointing pair in a box you ignored ten minutes ago is now the unlock. Glancing at the whole grid every five or six placements catches these. Our piece on the half-finished grid problem covers the broader version of this pattern.

When you find yourself spotting naked pairs and locked candidates without consciously hunting for them, you're ready for hard, where pencil marks stop being optional and the techniques start asking for more involved combinations. Medium is also the tier worth lingering at — it's the level where the puzzle stops being purely a scanning exercise and starts being something a little more like a small daily problem to think through. That feeling is most of why people keep playing.