EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 15: 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 15 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
29 of 54 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: XY-Chain (×6), Nice Loops/AICs (×4), Empty Rectangle (×2), Finned Fish (×2), W-Wing (×2), WXYZ-Wing (×2), 2-String Kite, Skyscraper, Sue de Coq, XY-Wing, 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 (24 of 29)
  1. Step 5 · 2-String Kite advanced
    Rules out 4 from R3C1.
  2. Step 6 · Empty Rectangle advanced
    Rules out 8 from R3C8.
  3. Step 7 · Finned Fish expert
    Rules out 8 from R2C7.
  4. Step 8 · ALS-XZ expert
    Rules out 8 from R8C5.
  5. Step 9 · Nice Loops/AICs expert
    Rules out 4 from R4C6.
  6. Step 10 · Nice Loops/AICs expert
    Rules out 5 from R4C7.
  7. Step 12 · Empty Rectangle advanced
    Rules out 8 from R5C6.
  8. Step 13 · WXYZ-Wing expert
    Rules out 8 from R7C5.
  9. Step 14 · Nice Loops/AICs expert
    Rules out 4 from R7C1.
  10. Step 17 · XY-Wing advanced
    Rules out 8 from R1C8.
  11. Step 18 · XY-Chain expert
    Rules out 2 from R3C8.
  12. Step 19 · Sue de Coq expert
    Rules out 1 from R1C8, R3C8, R5C7; 2 from R9C8.
  13. Step 23 · XY-Chain expert
    Rules out 8 from R1C5, R2C9.
  14. Step 24 · XY-Chain expert
    Rules out 3 from R2C9.
  15. Step 25 · XY-Chain expert
    Rules out 6 from R4C8.
  16. Step 26 · XY-Chain expert
    Rules out 8 from R5C8.
  17. Step 27 · ALS-XZ expert
    Rules out 8 from R3C5.
  18. Step 31 · WXYZ-Wing expert
    Rules out 1 from R3C4.
  19. Step 32 · ALS-XZ expert
    Rules out 3 from R1C3.
  20. Step 33 · Nice Loops/AICs expert
    Rules out 7 from R3C3.
  21. Step 36 · XY-Chain expert
    Rules out 1 from R3C5.
  22. Step 37 · ALS-XZ expert
    Rules out 3 from R3C2.
  23. Step 38 · ALS-XZ expert
    Rules out 3 from R3C1.
  24. Step 39 · ALS-XZ expert
    Rules out 4 from R3C3.

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.