EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 58: 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 58 of 150 in Extreme Sudoku 1
Difficulty
Expert 7 (expert and beyond), from the middle 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: Nice Loops/AICs (×4), W-Wing (×3), XY-Chain (×3), Finned Fish (×2), X-Wing/Swordfish (×2), 2-String Kite, Cell Forcing Chains, Skyscraper, Sue de Coq, WXYZ-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 6 · 2-String Kite advanced
    Rules out 5 from R2C7.
  2. Step 7 · W-Wing advanced
    Rules out 7 from R4C3.
  3. Step 8 · Finned Fish expert
    Rules out 6 from R1C7, R2C7.
  4. Step 9 · ALS-XZ expert
    Rules out 3 from R4C2, R5C2.
  5. Step 10 · WXYZ-Wing expert
    Rules out 7 from R4C1.
  6. Step 11 · ALS-XZ expert
    Rules out 7 from R2C3.
  7. Step 12 · Nice Loops/AICs expert
    Rules out 6 from R2C3.
  8. Step 13 · Nice Loops/AICs expert
    Rules out 6 from R2C2.
  9. Step 14 · Finned Fish expert
    Rules out 6 from R1C8.
  10. Step 15 · Nice Loops/AICs expert
    Rules out 2 from R2C1.
  11. Step 16 · Cell Forcing Chains expert
    Rules out 6 from R1C4, R2C9; 1 from R1C9, R2C1; 5 from R2C2.
  12. Step 17 · X-Wing/Swordfish advanced
    Rules out 6 from R4C3.
  13. Step 20 · Sue de Coq expert
    Rules out 2 from R1C2; 3 from R1C2; 7 from R2C7, R3C3.
  14. Step 25 · X-Wing/Swordfish advanced
    Rules out 5 from R7C2, R7C7.
  15. Step 26 · ALS-XZ expert
    Rules out 4 from R1C7.
  16. Step 27 · ALS-XZ expert
    Rules out 4 from R2C6.
  17. Step 28 · Nice Loops/AICs expert
    Rules out 3 from R1C8.
  18. Step 32 · Skyscraper advanced
    Rules out 4 from R8C3.
  19. Step 36 · W-Wing advanced
    Rules out 9 from R7C4.
  20. Step 37 · W-Wing advanced
    Rules out 8 from R2C4.
  21. Step 38 · XY-Chain expert
    Rules out 9 from R9C6.
  22. Step 41 · XY-Chain expert
    Rules out 1 from R8C8.
  23. Step 43 · XY-Chain expert
    Rules out 4 from R8C8.

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.