The Complete Solver is the capstone lesson of the entire Sudoku curriculum. Rather than introducing a new technique, this lesson challenges you to apply every technique you have learned — from basic singles to advanced chains — in a single, extremely difficult puzzle. The puzzle is specifically chosen to require techniques from every tier: beginner scanning, intermediate subsets, advanced fish and wings, and expert chains and uniqueness arguments.
This lesson serves as both a graduation exercise and a reference for how expert solvers approach a puzzle from scratch. You will see how to triage a grid, identify which techniques are applicable at each stage, and chain together multiple strategies to drive a puzzle to completion. The walkthrough demonstrates the full problem-solving workflow: start with singles and scanning, progress to subsets when singles dry up, apply fish and intersection techniques, and finally deploy chains and uniqueness arguments for the final breakthrough.
Completing this lesson means you have a working understanding of all 29 techniques in the curriculum and can combine them fluently. This is the mark of a complete Sudoku solver — someone who can tackle any standard puzzle regardless of difficulty rating.
Try It Yourself
Walk through each step of the the complete solver technique on a real puzzle. Follow the instructions and try entering the correct value when prompted.
Start by scanning for any obvious singles. Look for rows, columns, or boxes with only one empty cell. Apply Last Remaining Cell and Full House logic to fill in the easiest cells first.
Step-by-Step Guide
Begin with a full scan for Last Remaining Cells and Full Houses across all units.
Apply Cross-Hatching to place digits using row and column elimination.
Update all pencilmarks and scan for Naked and Hidden Singles.
Look for Pointing Pairs and Box/Line Reductions at box-line intersections.
Search for Naked and Hidden Pairs, Triples, and Quads to eliminate candidates.
Apply fish techniques: X-Wing, Swordfish, and their finned variants.
Use single-digit patterns: Skyscraper, 2-String Kite, Simple Coloring.
Deploy wing techniques: Y-Wing, XYZ-Wing, W-Wing.
Apply chain techniques: X-Cycles and XY-Chains for the final eliminations.
Check for Unique Rectangles and BUG patterns if the puzzle stalls.
Verify the completed solution satisfies all Sudoku constraints.
Think of this as your final exam: one puzzle that tests every tool in your toolkit, from the simplest to the most advanced.
Every well-formed Sudoku puzzle has a unique solution reachable through logical deduction. By mastering the full spectrum of techniques, you can always find the next logical step without guessing. This lesson proves that principle by walking through a complete solve using only logic.
When to use: Use this lesson as a reference whenever you encounter a puzzle that seems to require techniques from multiple tiers. The workflow demonstrated here — scanning, subsets, fish, wings, chains — is the standard approach for expert-level puzzles.
Common Mistakes to Avoid
Jumping to advanced techniques before exhausting simpler ones. Even in hard puzzles, most cells are solved with basic techniques.
Always start with full house and singles scanning. Apply intermediate subsets next. Only move to advanced and expert techniques when simpler methods yield no progress.
Losing track of which techniques have been tried at a given stage.
Develop a systematic checklist: singles → subsets → intersections → fish → wings → chains → uniqueness. Work through the list in order at each impasse.
Making a pencilmark error early that cascades into contradictions later.
Periodically verify your pencilmarks, especially after complex eliminations. One wrong mark can invalidate every subsequent deduction.
Quick Reference
- Pattern:
- A puzzle requiring techniques from every tier of difficulty
- Action:
- Apply techniques systematically: singles → subsets → fish → wings → chains
- Look for:
- A puzzle where no single technique category is sufficient