EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 49: 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 49 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
29 of 58 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 (×9), Finned Fish (×2), Skyscraper (×2), 2-String Kite, Empty Rectangle, WXYZ-Wing, XY-Chain, 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 (24 of 29)
  1. Step 3 · Skyscraper advanced
    Rules out 6 from R4C7, R9C8.
  2. Step 5 · Skyscraper advanced
    Rules out 8 from R1C7, R3C3.
  3. Step 6 · WXYZ-Wing expert
    Rules out 9 from R5C2.
  4. Step 7 · ALS-XZ expert
    Rules out 9 from R4C3.
  5. Step 8 · ALS-XZ expert
    Rules out 9 from R5C3.
  6. Step 9 · Nice Loops/AICs expert
    Rules out 6 from R5C4, R5C6, R5C9.
  7. Step 13 · Nice Loops/AICs expert
    Rules out 1 from R6C8.
  8. Step 15 · ALS-XZ expert
    Rules out 4 from R4C3, R8C1.
  9. Step 18 · ALS-XZ expert
    Rules out 9 from R1C2.
  10. Step 19 · ALS-XZ expert
    Rules out 2 from R2C2, R3C9.
  11. Step 23 · ALS-XZ expert
    Rules out 4 from R2C7.
  12. Step 24 · ALS-XZ expert
    Rules out 7 from R9C4, R9C6.
  13. Step 25 · Nice Loops/AICs expert
    Rules out 1 from R9C5.
  14. Step 26 · Nice Loops/AICs expert
    Rules out 1 from R9C8.
  15. Step 28 · Empty Rectangle advanced
    Rules out 1 from R1C7.
  16. Step 29 · Finned Fish expert
    Rules out 1 from R1C9.
  17. Step 31 · Nice Loops/AICs expert
    Rules out 5 from R2C8.
  18. Step 32 · XY-Wing advanced
    Rules out 6 from R3C8, R4C9.
  19. Step 35 · ALS-XZ expert
    Rules out 1 from R3C7.
  20. Step 36 · Nice Loops/AICs expert
    Rules out 1 from R1C4.
  21. Step 37 · Nice Loops/AICs expert
    Rules out 6 from R4C4.
  22. Step 38 · Nice Loops/AICs expert
    Rules out 1 from R9C4.
  23. Step 39 · Nice Loops/AICs expert
    Rules out 1 from R9C6.
  24. Step 40 · Finned Fish expert
    Rules out 1 from R1C5.

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.