EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 41: 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 41 of 150 in Extreme Sudoku 1
Difficulty
Expert 7 (expert and beyond), from the opening third of the book
Key technique
Nice Loops/AICs
Hard steps
20 of 43 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), W-Wing (×3), XY-Chain (×3), Finned Fish (×2), Cell Forcing Chains, Sue de Coq, WXYZ-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 (20)
  1. Step 6 · WXYZ-Wing expert
    Rules out 8 from R2C7, R3C7.
  2. Step 8 · W-Wing advanced
    Rules out 2 from R3C1, R3C2, R3C3.
  3. Step 9 · Nice Loops/AICs expert
    Rules out 5 from R8C3.
  4. Step 10 · Nice Loops/AICs expert
    Rules out 5 from R3C3.
  5. Step 11 · ALS-XZ expert
    Rules out 2 from R2C1.
  6. Step 12 · Nice Loops/AICs expert
    Rules out 8 from R9C9.
  7. Step 13 · Nice Loops/AICs expert
    Rules out 2 from R9C5.
  8. Step 14 · Nice Loops/AICs expert
    Rules out 2 from R9C2.
  9. Step 15 · Cell Forcing Chains expert
    Rules out 3 from R1C3.
  10. Step 19 · Finned Fish expert
    Rules out 2 from R9C6.
  11. Step 20 · Sue de Coq expert
    Rules out 3 from R2C3; 5 from R8C2; 8 from R8C2.
  12. Step 22 · W-Wing advanced
    Rules out 2 from R8C6.
  13. Step 23 · ALS-XZ expert
    Rules out 1 from R4C3.
  14. Step 25 · ALS-XZ expert
    Rules out 2 from R8C8.
  15. Step 26 · Finned Fish expert
    Rules out 2 from R7C6.
  16. Step 27 · XY-Chain expert
    Rules out 1 from R3C2, R5C3.
  17. Step 30 · W-Wing advanced
    Rules out 7 from R4C2, R5C7, R5C8.
  18. Step 32 · XY-Chain expert
    Rules out 9 from R7C3.
  19. Step 37 · X-Wing/Swordfish advanced
    Rules out 2 from R8C5.
  20. Step 38 · XY-Chain expert
    Rules out 8 from R3C2, R9C1.

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.