EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 52: 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 52 of 150 in Extreme Sudoku 1
Difficulty
Expert 6 (expert and beyond), from the middle third of the book
Key technique
ALS-XZ
Hard steps
20 of 46 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: WXYZ-Wing (×4), Nice Loops/AICs (×2), Skyscraper (×2), XY-Chain (×2), 2-String Kite, Cell Forcing Chains, Finned Fish, 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 (20)
  1. Step 4 · XYZ-Wing advanced
    Rules out 9 from R5C7.
  2. Step 5 · ALS-XZ expert
    Rules out 9 from R1C8.
  3. Step 6 · ALS-XZ expert
    Rules out 7 from R3C8.
  4. Step 7 · Nice Loops/AICs expert
    Rules out 6 from R1C7.
  5. Step 8 · Cell Forcing Chains expert
    Rules out 1 from R1C4, R2C5, R3C8; 7 from R1C8; 2 from R2C5.
  6. Step 10 · Finned Fish expert
    Rules out 2 from R3C9.
  7. Step 11 · WXYZ-Wing expert
    Rules out 9 from R3C5.
  8. Step 12 · ALS-XZ expert
    Rules out 9 from R1C7.
  9. Step 13 · ALS-XZ expert
    Rules out 9 from R8C8.
  10. Step 14 · WXYZ-Wing expert
    Rules out 7 from R8C9, R9C9.
  11. Step 17 · Skyscraper advanced
    Rules out 6 from R4C1.
  12. Step 19 · ALS-XZ expert
    Rules out 2 from R1C9, R4C7.
  13. Step 22 · WXYZ-Wing expert
    Rules out 2 from R3C6.
  14. Step 23 · Nice Loops/AICs expert
    Rules out 9 from R5C5.
  15. Step 27 · Skyscraper advanced
    Rules out 9 from R7C6, R9C9.
  16. Step 29 · 2-String Kite advanced
    Rules out 9 from R9C2.
  17. Step 31 · XY-Wing advanced
    Rules out 1 from R1C1.
  18. Step 33 · XY-Chain expert
    Rules out 2 from R1C7.
  19. Step 39 · WXYZ-Wing expert
    Rules out 9 from R1C4.
  20. Step 40 · XY-Chain expert
    Rules out 6 from R1C2, R9C1.

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.