EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 57: 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 57 of 150 in Extreme Sudoku 2
Difficulty
Expert 6 (expert and beyond), from the middle third of the book
Key technique
ALS-XZ
Hard steps
23 of 48 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: Nice Loops/AICs (×6), 2-String Kite (×2), Finned Fish (×2), W-Wing (×2), Cell Forcing Chains, WXYZ-Wing, 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 (23)
  1. Step 4 · ALS-XZ expert
    Rules out 1 from R7C3.
  2. Step 5 · Nice Loops/AICs expert
    Rules out 1 from R8C6.
  3. Step 6 · Nice Loops/AICs expert
    Rules out 8 from R1C5.
  4. Step 7 · Nice Loops/AICs expert
    Rules out 4 from R1C6.
  5. Step 9 · ALS-XZ expert
    Rules out 9 from R1C4.
  6. Step 10 · Cell Forcing Chains expert
    Rules out 8 from R1C2, R2C5, R8C6, R9C6; 1 from R1C6, R2C2, R5C3, R5C4 and 1 more; 9 from R1C6, R8C1.
  7. Step 13 · Finned Fish expert
    Rules out 9 from R5C3.
  8. Step 14 · Finned Fish expert
    Rules out 9 from R6C2.
  9. Step 15 · ALS-XZ expert
    Rules out 9 from R4C6, R5C6.
  10. Step 17 · WXYZ-Wing expert
    Rules out 1 from R6C2.
  11. Step 19 · Nice Loops/AICs expert
    Rules out 1 from R1C5.
  12. Step 20 · XY-Wing advanced
    Rules out 5 from R2C5.
  13. Step 21 · ALS-XZ expert
    Rules out 9 from R3C4, R5C5.
  14. Step 23 · Nice Loops/AICs expert
    Rules out 4 from R7C3.
  15. Step 25 · ALS-XZ expert
    Rules out 3 from R9C1.
  16. Step 30 · XY-Chain expert
    Rules out 9 from R3C5.
  17. Step 31 · ALS-XZ expert
    Rules out 3 from R5C9.
  18. Step 32 · Nice Loops/AICs expert
    Rules out 1 from R7C2.
  19. Step 37 · 2-String Kite advanced
    Rules out 6 from R5C9.
  20. Step 38 · 2-String Kite advanced
    Rules out 7 from R3C9.
  21. Step 40 · XYZ-Wing advanced
    Rules out 7 from R6C7.
  22. Step 41 · W-Wing advanced
    Rules out 7 from R4C7.
  23. Step 44 · W-Wing advanced
    Rules out 7 from R4C2.

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.