EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 43: 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 43 of 150 in Extreme Sudoku 1
Difficulty
Expert 5 (expert and beyond), from the opening third of the book
Key technique
Nice Loops/AICs
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: 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 (×3), 2-String Kite (×2), Empty Rectangle (×2), Finned Fish (×2), W-Wing (×2), Jellyfish, XY-Chain, 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 6 · Finned Fish expert
    Rules out 9 from R3C8, R3C9.
  2. Step 7 · ALS-XZ expert
    Rules out 6 from R3C1.
  3. Step 9 · ALS-XZ expert
    Rules out 2 from R2C8.
  4. Step 10 · Nice Loops/AICs expert
    Rules out 7 from R9C9.
  5. Step 11 · Empty Rectangle advanced
    Rules out 7 from R2C8.
  6. Step 12 · Nice Loops/AICs expert
    Rules out 7 from R9C8.
  7. Step 13 · Nice Loops/AICs expert
    Rules out 8 from R1C4.
  8. Step 15 · Finned Fish expert
    Rules out 1 from R6C1.
  9. Step 16 · ALS-XZ expert
    Rules out 5 from R5C6.
  10. Step 17 · Nice Loops/AICs expert
    Rules out 3 from R3C1.
  11. Step 22 · Nice Loops/AICs expert
    Rules out 6 from R9C1.
  12. Step 24 · Nice Loops/AICs expert
    Rules out 9 from R5C4.
  13. Step 25 · Jellyfish expert
    Rules out 9 from R1C6, R1C8, R3C1, R6C1 and 2 more.
  14. Step 29 · 2-String Kite advanced
    Rules out 4 from R6C1.
  15. Step 31 · W-Wing advanced
    Rules out 5 from R4C6.
  16. Step 33 · Empty Rectangle advanced
    Rules out 4 from R3C9.
  17. Step 34 · XYZ-Wing advanced
    Rules out 4 from R5C6.
  18. Step 35 · 2-String Kite advanced
    Rules out 4 from R8C3.
  19. Step 37 · XY-Chain expert
    Rules out 6 from R1C3, R8C1.
  20. Step 42 · W-Wing advanced
    Rules out 1 from R8C4.

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.