EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 20: step-by-step solution

Step through the whole solution, or skip to the hard parts. Blue digits are placed by the walkthrough; red strike-through marks a candidate being ruled out.

Puzzle
Sudoku, number 20 of 150 in Extreme Sudoku 3
Difficulty
Expert 5 (expert and beyond), from the opening third of the book
Key technique
ALS-XZ
Hard steps
23 of 49 steps need an advanced or expert technique

Blue digits are placed by the walkthrough. Red strike-through marks a candidate being ruled out. Cells are named by row and column: R3C5 is row 3, column 5. Arrow keys step too.

The key technique: ALS-XZ

Two almost-locked sets (n cells with n+1 candidates) share a restricted digit X. Then a digit Z common to both must be in one of them, so cells seeing all of its copies cannot be Z.

Other advanced and expert techniques in this solve: Nice Loops/AICs (×5), XY-Chain (×3), Skyscraper (×2), WXYZ-Wing (×2), 2-String Kite, Sue de Coq, XY-Wing.

Every move above the basics is listed on the sudoku techniques page, each with a one-sentence explanation and worked examples from the books.

The hard steps, in text (23)
  1. Step 7 · Skyscraper advanced
    Rules out 5 from R6C7, R9C9.
  2. Step 8 · Skyscraper advanced
    Rules out 8 from R1C5, R2C2.
  3. Step 10 · ALS-XZ expert
    Rules out 2 from R1C8, R3C8.
  4. Step 11 · ALS-XZ expert
    Rules out 7 from R3C7.
  5. Step 12 · ALS-XZ expert
    Rules out 6 from R9C5.
  6. Step 13 · Nice Loops/AICs expert
    Rules out 1 from R1C8.
  7. Step 14 · Nice Loops/AICs expert
    Rules out 4 from R2C4.
  8. Step 16 · ALS-XZ expert
    Rules out 4 from R8C8, R8C9.
  9. Step 17 · Nice Loops/AICs expert
    Rules out 8 from R2C5.
  10. Step 20 · WXYZ-Wing expert
    Rules out 1 from R8C2.
  11. Step 21 · ALS-XZ expert
    Rules out 1 from R8C8.
  12. Step 22 · ALS-XZ expert
    Rules out 4 from R7C8.
  13. Step 23 · ALS-XZ expert
    Rules out 1 from R8C9.
  14. Step 24 · ALS-XZ expert
    Rules out 4 from R7C7.
  15. Step 25 · Nice Loops/AICs expert
    Rules out 1 from R4C3.
  16. Step 29 · WXYZ-Wing expert
    Rules out 1 from R7C4.
  17. Step 30 · Nice Loops/AICs expert
    Rules out 4 from R1C1.
  18. Step 33 · Sue de Coq expert
    Rules out 4 from R3C9, R6C9; 1 from R7C7, R7C8, R9C7, R9C8; 7 from R8C8, R9C7, R9C8.
  19. Step 35 · XY-Chain expert
    Rules out 4 from R1C8, R3C8, R9C9.
  20. Step 38 · 2-String Kite advanced
    Rules out 1 from R6C5.
  21. Step 40 · XY-Chain expert
    Rules out 8 from R8C1.
  22. Step 42 · XY-Chain expert
    Rules out 7 from R3C9.
  23. Step 43 · XY-Wing advanced
    Rules out 1 from R9C9.

The book

Volume three: 150 new classic 9×9 grids, none repeated from books 1 or 2, ramping from hard to brutal.

150 new puzzles. Expert and beyond. Puzzles by M. J. Bailey. Paperback, 5 × 8 in, 196 pages, £9.99 / $11.99. Every solution in the book carries a QR code to its own walkthrough, so you can check one step without seeing the whole answer.

On Amazon from 8 Dec About the book

Try a free sample puzzle (PDF) · prints on A4 or US Letter

More step-by-step solutions: Extreme Sudoku 1 · Extreme Killer Sudoku 1 · Extreme Sudoku 2 · Extreme Killer Sudoku 2 · Extreme Killer Sudoku 3.