EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 19: 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 19 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
19 of 45 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), Finned Fish (×2), Skyscraper (×2), WXYZ-Wing (×2), XY-Chain (×2), Empty Rectangle.

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 (19)
  1. Step 7 · Empty Rectangle advanced
    Rules out 6 from R9C9.
  2. Step 8 · Finned Fish expert
    Rules out 3 from R3C7.
  3. Step 9 · Finned Fish expert
    Rules out 3 from R1C7, R1C9.
  4. Step 10 · WXYZ-Wing expert
    Rules out 5 from R8C7.
  5. Step 13 · ALS-XZ expert
    Rules out 3 from R2C9.
  6. Step 15 · ALS-XZ expert
    Rules out 5 from R9C6.
  7. Step 17 · XY-Chain expert
    Rules out 9 from R1C8, R9C9.
  8. Step 21 · WXYZ-Wing expert
    Rules out 3 from R3C1.
  9. Step 22 · Nice Loops/AICs expert
    Rules out 4 from R4C5.
  10. Step 23 · Nice Loops/AICs expert
    Rules out 3 from R5C1.
  11. Step 24 · Nice Loops/AICs expert
    Rules out 3 from R5C7.
  12. Step 25 · ALS-XZ expert
    Rules out 9 from R4C7, R5C1.
  13. Step 27 · Nice Loops/AICs expert
    Rules out 4 from R4C1.
  14. Step 28 · Nice Loops/AICs expert
    Rules out 4 from R7C1.
  15. Step 29 · Nice Loops/AICs expert
    Rules out 6 from R4C4.
  16. Step 30 · Skyscraper advanced
    Rules out 6 from R7C7.
  17. Step 33 · Nice Loops/AICs expert
    Rules out 2 from R1C8.
  18. Step 35 · XY-Chain expert
    Rules out 8 from R1C2.
  19. Step 42 · Skyscraper advanced
    Rules out 6 from R3C3, R4C1.

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.