Key Points
  • Advanced elimination is always structured — never random guessing
  • Apply techniques in order of complexity: fish → wings → chains → trial-and-inference
  • Each technique targets specific candidate patterns — learn to recognize the shape, not just the rule
  • A single advanced elimination often triggers a cascade of simpler ones that solves the puzzle
  • Most Expert puzzles require only one or two advanced moves — the rest follows from basics

Before You Go Advanced

Before applying advanced techniques, double-check: (1) all pencil marks are accurate, (2) no Hidden Singles remain, (3) no Locked Candidates patterns are present, (4) no Naked or Hidden Pairs exist. Advanced techniques build on a clean, fully updated candidate set. A missed basic move makes advanced patterns invisible.

Fish Patterns (X-Wing, Swordfish)

Look for a digit that appears in exactly 2 cells in each of 2 rows, and those cells are in the same 2 columns. This is an X-Wing — eliminate the digit from all other cells in those 2 columns. Extend to 3 rows and 3 columns for a Swordfish. Fish patterns are the most common advanced technique needed at Expert level.

Wing Patterns (XY-Wing, XYZ-Wing)

Find a pivot cell with candidates XY. Look for two pincer cells with XZ and YZ. Any cell seeing both pincers cannot hold Z — eliminate it. XYZ-Wing adds a third candidate to the pivot, increasing the scope of possible eliminations.

Alternating Inference Chains (AIC)

Build a chain of cells connected by alternating strong and weak links on a single digit. When the chain's endpoints see each other, you can make eliminations. When the chain forms a closed loop, every strong link becomes a confirmed placement. Learning to read AIC chains is the single biggest skill leap in advanced Sudoku.

Trial and Inference (Structured Bifurcation)

As a last resort: assume one of a bi-value cell's candidates and follow all logical consequences. If the assumption leads to a contradiction (empty cell, no cell for a digit in some unit), the other candidate is confirmed. This is not guessing — it is formal proof by contradiction. Use it sparingly, and always trace the full chain of consequences rather than stopping partway. Explore worked examples in the full techniques library.