EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 39: 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 39 of 150 in Extreme Sudoku 1
Difficulty
Expert 6 (expert and beyond), from the opening third of the book
Key technique
Nice Loops/AICs
Hard steps
24 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: Nice Loops/AICs

An alternating chain of strong and weak links. Whichever end is true, the conclusion holds, so the digit at the marked cell is ruled out.

Other advanced and expert techniques in this solve: ALS-XZ (×5), Finned Fish (×2), WXYZ-Wing (×2), XY-Chain (×2), 2-String Kite, Empty Rectangle, Skyscraper, Sue de Coq, W-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)
  1. Step 4 · WXYZ-Wing expert
    Rules out 7 from R2C5, R3C5, R6C4.
  2. Step 6 · WXYZ-Wing expert
    Rules out 3 from R4C5.
  3. Step 9 · Finned Fish expert
    Rules out 5 from R7C9.
  4. Step 10 · ALS-XZ expert
    Rules out 4 from R9C7.
  5. Step 12 · Nice Loops/AICs expert
    Rules out 9 from R6C8.
  6. Step 14 · Nice Loops/AICs expert
    Rules out 4 from R2C3.
  7. Step 15 · Nice Loops/AICs expert
    Rules out 4 from R5C1.
  8. Step 16 · Nice Loops/AICs expert
    Rules out 9 from R2C8.
  9. Step 17 · Nice Loops/AICs expert
    Rules out 4 from R3C3.
  10. Step 18 · Nice Loops/AICs expert
    Rules out 4 from R5C3.
  11. Step 19 · Nice Loops/AICs expert
    Rules out 3 from R4C3.
  12. Step 20 · 2-String Kite advanced
    Rules out 3 from R7C6.
  13. Step 21 · Finned Fish expert
    Rules out 3 from R9C6.
  14. Step 22 · Sue de Coq expert
    Rules out 5 from R8C7, R9C7.
  15. Step 24 · X-Wing/Swordfish advanced
    Rules out 5 from R3C5, R9C5.
  16. Step 25 · ALS-XZ expert
    Rules out 1 from R9C6.
  17. Step 26 · ALS-XZ expert
    Rules out 7 from R2C6, R3C6, R9C4.
  18. Step 29 · ALS-XZ expert
    Rules out 9 from R2C6.
  19. Step 30 · ALS-XZ expert
    Rules out 9 from R5C5.
  20. Step 31 · XY-Chain expert
    Rules out 8 from R4C6, R6C3.
  21. Step 33 · XY-Chain expert
    Rules out 9 from R1C4, R3C4.
  22. Step 37 · Empty Rectangle advanced
    Rules out 3 from R3C2.
  23. Step 38 · W-Wing advanced
    Rules out 9 from R3C6, R8C5.
  24. Step 40 · Skyscraper advanced
    Rules out 3 from R5C5.

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.