Once you conquer medium puzzles, you will inevitably hit a wall on hard grids. Scanning and singles stop producing moves; the board feels locked. This is the moment most players either give up — or level up.

Here's the mental shift that defines advanced play: beginner techniques find answers, advanced techniques eliminate candidates. On a hard puzzle you'll often make ten eliminations before placing a single digit — and then five digits fall at once. Everything below assumes you're keeping full pencil marks (all legal candidates noted in each unsolved cell); on hard grids, that bookkeeping is the game.

First, master the humble pairs

Before the famous exotic patterns, two workhorse techniques solve more hard puzzles than everything else combined:

• Naked pairs. If two cells in the same row, column, or box contain exactly the same two candidates — say both are "3 or 8" — then 3 and 8 are spoken for. Erase them from every other cell in that region. The pair itself stays unresolved, but the eliminations elsewhere frequently crack the region open.
• Pointing pairs (box–line reduction). If, within one box, all remaining candidates for a digit sit in a single row or column, then that digit must occupy that row/column inside that box — so erase it from the rest of the row or column outside the box. This is the technique that most often un-sticks a "locked" medium-hard grid.

The X-Wing

The most famous advanced pattern. Look at one digit — say 7 — and find two rows in which the 7 has exactly two possible cells, and those cells sit in the same two columns. The four cells form the corners of a rectangle (the "X" is the pair of diagonals).

The logic: each of the two rows must contain a 7 in one of the two columns. Between them, the two rows will use up both columns' 7s — one each, diagonally. Therefore no other cell in those two columns can be a 7, and you can erase 7 from every other cell in both columns. (The same works with rows and columns swapped.) One clean X-Wing elimination often triggers a chain of singles that finishes the puzzle.

The Swordfish

A Swordfish is an X-Wing stretched to three rows and three columns: a digit restricted, in three different rows, to cells that all fall within the same three columns. The conclusion is identical in spirit — those three columns' copies of the digit are fully claimed by the three rows, so the candidate can be erased from the rest of all three columns.

Swordfish are rarer and harder to spot than X-Wings. The practical search method: pick a digit, mark which columns it can occupy in each row, and look for three rows whose combined column sets total exactly three columns. It feels mechanical at first, and then one day your eyes just see it.

The Y-Wing (XY-Wing)

The Y-Wing relies on bi-value cells — cells down to exactly two candidates. You need a "pivot" cell containing XY that can see two "wing" cells containing XZ and YZ. Whichever value the pivot takes, one of the wings is forced to be Z. Conclusion: any cell that can see both wings cannot be Z, and Z can be erased from it.

Concrete example: pivot holds {4,7}, one wing holds {4,2}, the other {7,2}. If the pivot is 4, the first wing becomes 2; if the pivot is 7, the second wing becomes 2. Either way, a 2 lands in one of the wings — so a cell seeing both wings can't be 2. Y-Wings are the gateway to the whole family of chain-based techniques used on expert grids.

Learn them in this order

1. Naked pairs → pointing pairs. Cheap to spot, constantly useful. Drill these until automatic.
2. X-Wing. Your first "pattern over the whole board" technique.
3. Y-Wing. Introduces pivot/wing logic and prepares you for chains.
4. Swordfish. Rare but decisive; by this point your candidate discipline can support the search.

All four boil down to the same principle: a candidate's presence in one place mathematically outlaws it somewhere else. You're no longer asking "what goes here?" but "what can't go there?" — and hard Sudoku is precisely the art of the second question.

Practising without frustration

Don't expect to spot a Swordfish in the wild on day one. A better regimen: play our Hard mode (23-clue grids) with full pencil marks and hunt specifically for one technique per session — today only X-Wings, tomorrow only pairs. Targeted hunting builds the visual memory far faster than general solving. And when a grid defeats you, that's fine: use a hint, see what you missed, and the pattern will be easier to see next time. The breakthrough moment when you crack your first "impossible" grid is one of the most satisfying feelings in puzzling.