EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 133: 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 133 of 150 in Extreme Sudoku 1
Difficulty
Expert 7 (expert and beyond), from the final, hardest third of the book
Key technique
ALS-XZ
Hard steps
28 of 60 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 (×4), Nice Loops/AICs (×3), 2-String Kite (×2), XY-Wing (×2), Cell Forcing Chains, Empty Rectangle, Finned Fish, Sue de Coq, W-Wing, WXYZ-Wing, X-Wing/Swordfish, 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 28)
  1. Step 4 · 2-String Kite advanced
    Rules out 1 from R1C6.
  2. Step 6 · 2-String Kite advanced
    Rules out 2 from R5C6.
  3. Step 7 · WXYZ-Wing expert
    Rules out 2 from R4C8.
  4. Step 9 · ALS-XZ expert
    Rules out 2 from R9C4.
  5. Step 11 · ALS-XZ expert
    Rules out 5 from R6C6.
  6. Step 12 · Nice Loops/AICs expert
    Rules out 2 from R2C8.
  7. Step 13 · Nice Loops/AICs expert
    Rules out 6 from R7C3.
  8. Step 14 · Cell Forcing Chains expert
    Rules out 2 from R1C6.
  9. Step 17 · ALS-XZ expert
    Rules out 8 from R3C9.
  10. Step 18 · ALS-XZ expert
    Rules out 6 from R2C3.
  11. Step 19 · ALS-XZ expert
    Rules out 1 from R5C3.
  12. Step 22 · Nice Loops/AICs expert
    Rules out 7 from R4C2.
  13. Step 26 · Empty Rectangle advanced
    Rules out 8 from R8C9.
  14. Step 28 · XYZ-Wing advanced
    Rules out 5 from R6C5.
  15. Step 30 · Finned Fish expert
    Rules out 6 from R3C9.
  16. Step 31 · Sue de Coq expert
    Rules out 3 from R4C8; 7 from R4C8.
  17. Step 32 · ALS-XZ expert
    Rules out 3 from R7C4, R7C5.
  18. Step 34 · XY-Wing advanced
    Rules out 3 from R6C4.
  19. Step 36 · W-Wing advanced
    Rules out 5 from R7C1.
  20. Step 37 · ALS-XZ expert
    Rules out 4 from R1C1.
  21. Step 38 · ALS-XZ expert
    Rules out 6 from R8C3.
  22. Step 39 · ALS-XZ expert
    Rules out 6 from R1C1, R5C1.
  23. Step 42 · XY-Chain expert
    Rules out 8 from R9C8.
  24. Step 43 · X-Wing/Swordfish advanced
    Rules out 8 from R1C2, R4C2, R4C9.

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.