Solving master classic sudoku

Master classic sudoku is the tier where chain-based techniques start carrying real weight. The X-wings and swordfish from expert remain in rotation, but most master puzzles can't be solved on subsets and fish alone — they require linking cells through their candidate sets, following the implication of one digit's placement to a forced placement somewhere else on the grid. The techniques sound exotic when first described, and they look exotic for the first ten or twenty puzzles. After that, the patterns become as visually salient as naked pairs were at medium. The eye learns what it scans for.

The XY-wing as the gateway technique

The XY-wing is the chain-based technique most solvers meet first at master. Three cells: a "pivot" cell with two candidates X and Y, and two "wing" cells, each sharing one candidate with the pivot. One wing has X and Z; the other has Y and Z. Whatever digit ends up in the pivot — X or Y — one of the wings ends up holding Z. The cells that share a unit with both wings can therefore have Z eliminated, because Z must end up in one of the two wings.

Reading this from a definition is harder than spotting it on a real grid. The visual pattern: three cells forming a bent line, all carrying short candidate sets, with one digit (Z) appearing in both wing cells but not the pivot. Practice makes the pattern obvious quickly. Most solvers find XY-wings on most master puzzles after two or three weeks of dedicated solving at this tier.

Single-digit patterns

The skyscraper, 2-string kite, and empty rectangle are three named patterns that all reduce to the same underlying logic: a strong link in one direction (a digit can only go in two places in a region) chained to another strong link in a different direction, propagating an elimination across the grid. The geometry of where the strong links meet determines the name. From the solver's perspective, these are all the same technique applied to slightly different configurations.

What makes single-digit patterns useful at master: they require no notation beyond the standard pencil marks, but they break stalls that subsets and fish can't. When a master puzzle has resisted X-wings and naked triples for fifteen minutes, the move waiting is often a skyscraper. Walking the grid by digit, looking for digits whose only positions in two regions form a recognisable strong-link configuration, surfaces them.

Jellyfish and beyond

Jellyfish is the four-row generalisation of the X-wing/swordfish family. Four rows where a digit's positions are confined to the same four columns — the digit must occupy four of the sixteen cells, one per row and one per column. Other cells in those four columns lose the digit. Jellyfish is rare even at master — most solvers see one every five or six puzzles — but when it does fire, it's often the only move that breaks the puzzle. Recognising one is more about understanding the family pattern than about memorising a separate technique.

When master stalls

Master stalls in two characteristic ways, both rooted in notation rather than technique.

Pencil-mark drift. Master puzzles routinely take 25 to 45 minutes, and over that time the candidate notes accumulate small errors. A cell that should have lost a candidate after a chain elimination still has it; a cell that briefly held a single value got its other candidates re-pencilled by mistake. After 30 minutes the notation no longer reflects the grid's actual state, and the next move appears to be missing when it's actually being hidden by stale notes. The fix is the audit pass — walk every empty cell and verify its candidates against the row, column, and box. Three minutes, often surfaces the missed move directly.

Chain-tracking errors. The chain-based techniques require holding a temporary if-then state in your head: "if this cell is X, then that cell is Y, then this third cell is Z." Solvers who try to spot these by inspection without writing intermediate notes occasionally get the chain wrong, and the resulting elimination is invalid. The fix is to physically mark the chain on the grid (a small dot or arrow next to each cell) so the reasoning is visible. Most master solvers eventually adopt some form of chain-marking notation.

Two habits to drop

Half-pencil-marking. The cost of skipping pencil marks on cells that look "about to resolve" was high at expert and is higher at master. Chain-based techniques span the entire grid, and a missed pencil mark on a cell on the opposite side of the grid can hide the chain entirely. Full pencil marks across every empty cell from the start.

Treating chains as guesses. Chain-based techniques are sometimes confused with guessing — "what if the cell were X" — but the difference is that guessing produces a result conditional on an assumption, while a chain follows logic that's true regardless of which case is actually correct. If both branches of a strong link lead to the same elimination, the elimination stands without anyone needing to know which branch is true. That distinction matters: guesses introduce errors when wrong, chains never do.

When the named techniques start firing on first inspection and the chain-tracking notation feels natural, you're ready for extreme, where unique rectangles and longer forcing chains enter the rotation. Master is the tier most experienced solvers settle at as their daily practice — the puzzles take real attention but rarely defeat them, and the satisfaction is the steady tempo of a tier where every solve still asks for something new.