EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 12: 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 12 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
22 of 50 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), Finned Fish (×4), W-Wing (×2), 2-String Kite, Nice Loops/AICs, 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 (22)
  1. Step 4 · 2-String Kite advanced
    Rules out 9 from R9C9.
  2. Step 5 · Finned Fish expert
    Rules out 1 from R4C3.
  3. Step 6 · Finned Fish expert
    Rules out 9 from R3C8.
  4. Step 7 · Finned Fish expert
    Rules out 9 from R9C7.
  5. Step 8 · WXYZ-Wing expert
    Rules out 7 from R8C4, R9C4.
  6. Step 10 · ALS-XZ expert
    Rules out 1 from R7C5.
  7. Step 11 · ALS-XZ expert
    Rules out 4 from R7C5.
  8. Step 12 · ALS-XZ expert
    Rules out 4 from R4C4.
  9. Step 14 · Finned Fish expert
    Rules out 4 from R1C3.
  10. Step 15 · Nice Loops/AICs expert
    Rules out 5 from R9C4.
  11. Step 19 · ALS-XZ expert
    Rules out 9 from R1C3, R3C7.
  12. Step 20 · ALS-XZ expert
    Rules out 4 from R1C1.
  13. Step 22 · XY-Wing advanced
    Rules out 6 from R3C7.
  14. Step 26 · W-Wing advanced
    Rules out 1 from R4C6.
  15. Step 29 · XY-Chain expert
    Rules out 2 from R2C2.
  16. Step 31 · XY-Chain expert
    Rules out 2 from R1C7, R2C1.
  17. Step 33 · XY-Chain expert
    Rules out 9 from R3C3, R4C2.
  18. Step 35 · XY-Chain expert
    Rules out 9 from R5C5.
  19. Step 38 · XY-Chain expert
    Rules out 7 from R9C6.
  20. Step 39 · W-Wing advanced
    Rules out 1 from R9C3.
  21. Step 40 · XY-Chain expert
    Rules out 1 from R9C9.
  22. Step 41 · ALS-XZ expert
    Rules out 9 from R8C5, R9C8.

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.