EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 9: 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 9 of 150 in Extreme Sudoku 1
Difficulty
Expert 5 (expert and beyond), from the opening third of the book
Key technique
ALS-XZ
Hard steps
18 of 40 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 (×3), 2-String Kite (×2), W-Wing (×2), Coloring/Multi-coloring, Empty Rectangle, Finned Fish, WXYZ-Wing, 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 (18)
  1. Step 3 · 2-String Kite advanced
    Rules out 4 from R3C4.
  2. Step 4 · Empty Rectangle advanced
    Rules out 4 from R9C4.
  3. Step 5 · XY-Wing advanced
    Rules out 9 from R6C5, R9C4.
  4. Step 6 · ALS-XZ expert
    Rules out 3 from R7C7, R9C7.
  5. Step 8 · Coloring/Multi-coloring expert
    Rules out 4 from R7C7, R9C7.
  6. Step 13 · 2-String Kite advanced
    Rules out 9 from R6C6.
  7. Step 15 · W-Wing advanced
    Rules out 2 from R3C2.
  8. Step 16 · ALS-XZ expert
    Rules out 8 from R3C2.
  9. Step 18 · Finned Fish expert
    Rules out 7 from R9C3.
  10. Step 19 · XY-Chain expert
    Rules out 7 from R2C1.
  11. Step 20 · WXYZ-Wing expert
    Rules out 9 from R6C3.
  12. Step 21 · ALS-XZ expert
    Rules out 2 from R1C8.
  13. Step 22 · ALS-XZ expert
    Rules out 2 from R1C2.
  14. Step 24 · ALS-XZ expert
    Rules out 7 from R7C3.
  15. Step 25 · ALS-XZ expert
    Rules out 4 from R7C5.
  16. Step 30 · XY-Chain expert
    Rules out 8 from R1C3, R7C2.
  17. Step 32 · XY-Chain expert
    Rules out 6 from R1C1, R4C3.
  18. Step 35 · W-Wing advanced
    Rules out 3 from R9C4.

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.