EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, 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 2
Difficulty
Expert 7 (expert and beyond), from the opening third of the book
Key technique
ALS-XZ
Hard steps
21 of 39 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: ALS-XZ

Two almost-locked sets (n cells with n+1 candidates) share a restricted digit X. Then a digit Z common to both must be in one of them, so cells seeing all of its copies cannot be Z.

Other advanced and expert techniques in this solve: Empty Rectangle (×4), Nice Loops/AICs (×4), WXYZ-Wing (×3), 2-String Kite, Coloring/Multi-coloring, Finned Fish, Sue de Coq, X-Wing/Swordfish, XY-Chain.

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 (21)
  1. Step 5 · X-Wing/Swordfish advanced
    Rules out 2 from R2C2, R4C2, R4C8, R7C8.
  2. Step 6 · Empty Rectangle advanced
    Rules out 4 from R7C8.
  3. Step 7 · WXYZ-Wing expert
    Rules out 7 from R9C4.
  4. Step 12 · ALS-XZ expert
    Rules out 9 from R5C3.
  5. Step 13 · WXYZ-Wing expert
    Rules out 1 from R7C3.
  6. Step 14 · Nice Loops/AICs expert
    Rules out 6 from R2C3.
  7. Step 15 · Nice Loops/AICs expert
    Rules out 9 from R2C1.
  8. Step 16 · ALS-XZ expert
    Rules out 6 from R4C1.
  9. Step 17 · Nice Loops/AICs expert
    Rules out 7 from R2C2.
  10. Step 18 · Empty Rectangle advanced
    Rules out 7 from R9C5.
  11. Step 20 · ALS-XZ expert
    Rules out 9 from R2C3.
  12. Step 22 · WXYZ-Wing expert
    Rules out 1 from R4C1.
  13. Step 23 · Empty Rectangle advanced
    Rules out 1 from R5C8.
  14. Step 24 · Sue de Coq expert
    Rules out 1 from R4C3, R8C3; 6 from R4C3.
  15. Step 29 · 2-String Kite advanced
    Rules out 1 from R8C8.
  16. Step 30 · Empty Rectangle advanced
    Rules out 7 from R8C4.
  17. Step 31 · Finned Fish expert
    Rules out 7 from R4C8, R4C9.
  18. Step 32 · ALS-XZ expert
    Rules out 7 from R2C3.
  19. Step 33 · Nice Loops/AICs expert
    Rules out 7 from R4C6.
  20. Step 34 · Coloring/Multi-coloring expert
    Rules out 7 from R8C6.
  21. Step 37 · XY-Chain expert
    Rules out 7 from R9C2.

The book

Volume two: 150 new classic 9×9 grids, none repeated from book 1, ramping from hard to brutal.

150 new 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 Sudoku 1 · Extreme Killer Sudoku 1 · Extreme Killer Sudoku 2 · Extreme Sudoku 3 · Extreme Killer Sudoku 3.