EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 16: 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 16 of 150 in Extreme Sudoku 1
Difficulty
Expert 6 (expert and beyond), from the opening third of the book
Key technique
ALS-XZ
Hard steps
23 of 47 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: W-Wing (×5), Empty Rectangle (×3), XY-Chain (×3), 2-String Kite, Finned Fish, Nice Loops/AICs, Sue de Coq, WXYZ-Wing, X-Wing/Swordfish, XYZ-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 5 · Empty Rectangle advanced
    Rules out 5 from R2C1.
  2. Step 6 · W-Wing advanced
    Rules out 1 from R2C7.
  3. Step 7 · W-Wing advanced
    Rules out 4 from R1C8, R8C9.
  4. Step 8 · Finned Fish expert
    Rules out 4 from R2C1.
  5. Step 10 · 2-String Kite advanced
    Rules out 4 from R4C8.
  6. Step 11 · WXYZ-Wing expert
    Rules out 9 from R1C5.
  7. Step 12 · Sue de Coq expert
    Rules out 1 from R8C7; 6 from R8C7.
  8. Step 13 · Empty Rectangle advanced
    Rules out 6 from R6C3.
  9. Step 14 · W-Wing advanced
    Rules out 4 from R3C7.
  10. Step 15 · ALS-XZ expert
    Rules out 1 from R7C9.
  11. Step 16 · ALS-XZ expert
    Rules out 7 from R7C2.
  12. Step 17 · XY-Chain expert
    Rules out 6 from R7C7, R7C9.
  13. Step 23 · XY-Chain expert
    Rules out 1 from R3C5.
  14. Step 24 · Nice Loops/AICs expert
    Rules out 1 from R1C8.
  15. Step 29 · ALS-XZ expert
    Rules out 4 from R2C2.
  16. Step 30 · ALS-XZ expert
    Rules out 6 from R5C2, R7C3.
  17. Step 32 · Empty Rectangle advanced
    Rules out 5 from R1C5.
  18. Step 33 · ALS-XZ expert
    Rules out 1 from R1C5, R8C6.
  19. Step 35 · W-Wing advanced
    Rules out 7 from R1C2.
  20. Step 36 · W-Wing advanced
    Rules out 7 from R4C1.
  21. Step 38 · XY-Chain expert
    Rules out 4 from R3C2.
  22. Step 40 · X-Wing/Swordfish advanced
    Rules out 5 from R2C6, R7C3.
  23. Step 44 · XYZ-Wing advanced
    Rules out 3 from R1C5.

The book

Classic 9×9 sudoku with the warm-up taken out. Every grid sits at the top of the expert range or beyond it, and the book ramps from hard to brutal.

150 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.

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