EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 134: 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 134 of 150 in Extreme Sudoku 1
Difficulty
Expert 8 (expert and beyond), from the final, hardest third of the book
Key technique
ALS-XZ
Hard steps
39 of 63 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 (×11), XY-Chain (×3), Empty Rectangle (×2), Finned Fish (×2), W-Wing (×2), 2-String Kite, Cell Forcing Chains, Coloring/Multi-coloring, Sue de Coq, WXYZ-Wing, X-Wing/Swordfish.

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 39)
  1. Step 1 · WXYZ-Wing expert
    Rules out 9 from R9C5.
  2. Step 2 · ALS-XZ expert
    Rules out 9 from R3C6.
  3. Step 3 · ALS-XZ expert
    Rules out 7 from R3C6.
  4. Step 4 · ALS-XZ expert
    Rules out 3 from R9C5.
  5. Step 6 · ALS-XZ expert
    Rules out 1 from R4C5.
  6. Step 7 · Nice Loops/AICs expert
    Rules out 9 from R3C5.
  7. Step 8 · Nice Loops/AICs expert
    Rules out 7 from R4C5.
  8. Step 13 · 2-String Kite advanced
    Rules out 9 from R8C1.
  9. Step 14 · Empty Rectangle advanced
    Rules out 9 from R8C9.
  10. Step 15 · Finned Fish expert
    Rules out 4 from R9C1.
  11. Step 16 · Coloring/Multi-coloring expert
    Rules out 9 from R7C3, R9C3.
  12. Step 17 · ALS-XZ expert
    Rules out 4 from R6C2.
  13. Step 19 · XY-Chain expert
    Rules out 7 from R5C1.
  14. Step 20 · ALS-XZ expert
    Rules out 5 from R3C8.
  15. Step 21 · ALS-XZ expert
    Rules out 4 from R2C4, R3C9.
  16. Step 23 · ALS-XZ expert
    Rules out 7 from R7C7.
  17. Step 24 · ALS-XZ expert
    Rules out 3 from R7C7, R9C7.
  18. Step 25 · ALS-XZ expert
    Rules out 8 from R6C9.
  19. Step 26 · ALS-XZ expert
    Rules out 5 from R4C9.
  20. Step 27 · Nice Loops/AICs expert
    Rules out 9 from R9C7.
  21. Step 29 · Nice Loops/AICs expert
    Rules out 8 from R7C7.
  22. Step 30 · Cell Forcing Chains expert
    Rules out 2 from R1C4.
  23. Step 32 · Nice Loops/AICs expert
    Rules out 3 from R1C9.
  24. Step 33 · ALS-XZ expert
    Rules out 6 from R6C9.

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.