Overview
The speaker demonstrates an advanced Sudoku solving technique, focusing on set equivalence theory, to reduce a complex puzzle to just one required advanced strategy. The walkthrough illustrates logical candidate restrictions, highlights pattern recognition, and explains each key deduction step by step.
Initial Setup and Marking Candidates
- Restrict sixes in column one and row one, identifying two candidate spots per block.
- Mark pointing pairs and hidden pairs for sixes, threes, fours, ones, and twos across key blocks.
- Use nine and four as pointing pairs to restrict candidate placement further.
- Identify and mark naked and hidden pairs/triples to limit pencil marks.
Introduction to Set Equivalence Theory
- Notice pattern in rows two and six and analyze possible candidates.
- Color-code rows for digits 1–4 and columns for other candidates to illustrate set groupings.
- Apply set equivalence theory: equate the number of completed sets between colored rows and columns to create new logical restrictions.
- Deduce that only certain digits (including exactly one six and one nine) can fit in remaining cells; eliminate impossible candidates.
Key Deductions Using Set Theory
- Eliminate options for specific cells based on set equivalence; restrict some cells to just six or nine.
- Make crucial placements and further restrict the puzzle by updating pencil marks.
- Progressively solve for eights, sevens, and other numbers using the implications of the set theory setup.
Cascading Solving Steps
- Use newly solved digits to eliminate additional candidates in related rows, columns, and blocks.
- Identify and apply more straightforward techniques like naked/hidden pairs as the grid becomes increasingly constrained.
- Solve for multiple numbers in sequence, unravelling larger sections of the puzzle.
Application of the Skyscraper Advanced Strategy
- Recognize a skyscraper pattern with fours across row five and row nine.
- Use the conjugate pair logic to eliminate fours from specific cells, enabling more direct solves.
- Complete the puzzle with straightforward eliminations and placements following the application of the skyscraper technique.
Puzzle Crafting Insights and Closing
- Setter typically spends 3–20 hours on puzzle creation, ensuring difficulty and uniqueness.
- Quality control includes re-testing and refinement for both classic and variant Sudoku puzzles.
- Speaker encourages viewers to join their puzzle club and learn more advanced strategies.
Decisions
- Utilize set equivalence theory as the core technique to restrict candidates and solve the puzzle.
- Apply the skyscraper strategy on the number four as the final advanced step to finish the grid.
Action Items
- TBD – Audience: Review supplementary material on set equivalence theory and skyscraper techniques for further learning.
- TBD – Interested viewers: Consider joining the puzzle club to access more advanced puzzles and tutorials.