EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 42: 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 42 of 150 in Extreme Sudoku 1
Difficulty
Expert 7 (expert and beyond), from the opening third of the book
Key technique
WXYZ-Wing
Hard steps
20 of 44 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: WXYZ-Wing

Four cells holding four digits between them, where only one digit is not confined. That digit is removed from cells that see all its copies.

Other advanced and expert techniques in this solve: W-Wing (×3), ALS-XZ (×2), Nice Loops/AICs (×2), 2-String Kite, Cell Forcing Chains, Empty Rectangle, Finned Fish, Skyscraper, Sue de Coq, X-Wing/Swordfish, XY-Chain, XY-Wing, 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 4 · 2-String Kite advanced
    Rules out 1 from R5C8.
  2. Step 5 · Empty Rectangle advanced
    Rules out 5 from R7C7.
  3. Step 6 · WXYZ-Wing expert
    Rules out 9 from R1C5.
  4. Step 7 · Sue de Coq expert
    Rules out 4 from R2C1, R5C1, R6C1; 1 from R5C1, R6C1; 3 from R8C3, R9C3.
  5. Step 8 · Nice Loops/AICs expert
    Rules out 4 from R5C6.
  6. Step 10 · WXYZ-Wing expert
    Rules out 1 from R4C5.
  7. Step 11 · WXYZ-Wing expert
    Rules out 9 from R7C5.
  8. Step 12 · ALS-XZ expert
    Rules out 4 from R6C9.
  9. Step 13 · Nice Loops/AICs expert
    Rules out 4 from R6C3.
  10. Step 14 · Cell Forcing Chains expert
    Rules out 8 from R1C2.
  11. Step 21 · XYZ-Wing advanced
    Rules out 5 from R6C7.
  12. Step 22 · W-Wing advanced
    Rules out 3 from R7C7, R8C5.
  13. Step 24 · W-Wing advanced
    Rules out 4 from R7C9.
  14. Step 25 · Finned Fish expert
    Rules out 9 from R6C4.
  15. Step 26 · ALS-XZ expert
    Rules out 9 from R7C6.
  16. Step 28 · XY-Wing advanced
    Rules out 9 from R4C9.
  17. Step 33 · X-Wing/Swordfish advanced
    Rules out 1 from R5C5.
  18. Step 34 · Skyscraper advanced
    Rules out 5 from R2C1, R6C3.
  19. Step 37 · XY-Chain expert
    Rules out 9 from R4C4.
  20. Step 40 · W-Wing advanced
    Rules out 8 from R8C8, R9C4, R9C6.

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.