EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 85: 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 85 of 150 in Extreme Sudoku 2
Difficulty
Expert 7 (expert and beyond), from the middle third of the book
Key technique
ALS-XZ
Hard steps
19 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: 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: XY-Chain (×3), 2-String Kite (×2), Finned Fish (×2), XY-Wing (×2), Cell Forcing Chains, Empty Rectangle, Nice Loops/AICs, Sue de Coq, WXYZ-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 (19)
  1. Step 5 · 2-String Kite advanced
    Rules out 2 from R1C4.
  2. Step 6 · Finned Fish expert
    Rules out 2 from R3C4.
  3. Step 8 · Empty Rectangle advanced
    Rules out 4 from R9C3.
  4. Step 9 · ALS-XZ expert
    Rules out 6 from R6C9.
  5. Step 10 · ALS-XZ expert
    Rules out 2 from R2C4, R4C7.
  6. Step 14 · WXYZ-Wing expert
    Rules out 4 from R5C5.
  7. Step 15 · Sue de Coq expert
    Rules out 4 from R1C5; 7 from R1C5, R3C5; 6 from R5C4, R9C4.
  8. Step 16 · Nice Loops/AICs expert
    Rules out 4 from R8C2, R9C2.
  9. Step 18 · Cell Forcing Chains expert
    Rules out 7 from R2C5.
  10. Step 22 · XY-Wing advanced
    Rules out 7 from R1C1.
  11. Step 23 · XY-Chain expert
    Rules out 7 from R1C2.
  12. Step 24 · ALS-XZ expert
    Rules out 7 from R3C1, R3C2.
  13. Step 27 · ALS-XZ expert
    Rules out 8 from R8C1.
  14. Step 29 · XY-Chain expert
    Rules out 9 from R3C4.
  15. Step 30 · ALS-XZ expert
    Rules out 6 from R8C5.
  16. Step 31 · XY-Wing advanced
    Rules out 9 from R3C5.
  17. Step 35 · Finned Fish expert
    Rules out 7 from R4C8.
  18. Step 38 · 2-String Kite advanced
    Rules out 9 from R5C5.
  19. Step 39 · XY-Chain expert
    Rules out 2 from R1C2, R8C1.

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.