EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 37: 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 37 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
22 of 51 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 (×4), XY-Chain (×2), 2-String Kite, BUG+1, Cell Forcing Chains, Empty Rectangle, Finned Fish, Skyscraper, Sue de Coq, Unique Rectangles, WXYZ-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 (22)
  1. Step 7 · Empty Rectangle advanced
    Rules out 9 from R3C3.
  2. Step 8 · Finned Fish expert
    Rules out 5 from R3C3.
  3. Step 12 · WXYZ-Wing expert
    Rules out 2 from R1C1.
  4. Step 13 · Sue de Coq expert
    Rules out 5 from R7C9, R8C9, R9C9.
  5. Step 15 · 2-String Kite advanced
    Rules out 8 from R9C8.
  6. Step 16 · ALS-XZ expert
    Rules out 9 from R1C1, R8C2.
  7. Step 17 · ALS-XZ expert
    Rules out 5 from R1C3, R8C2.
  8. Step 18 · ALS-XZ expert
    Rules out 6 from R8C4, R9C4.
  9. Step 19 · Nice Loops/AICs expert
    Rules out 8 from R1C9.
  10. Step 23 · Nice Loops/AICs expert
    Rules out 9 from R1C7.
  11. Step 25 · Unique Rectangles advanced
    Rules out 2 from R4C9; 5 from R4C9.
  12. Step 28 · ALS-XZ expert
    Rules out 6 from R8C5.
  13. Step 29 · ALS-XZ expert
    Rules out 6 from R8C6.
  14. Step 30 · ALS-XZ expert
    Rules out 8 from R9C6.
  15. Step 31 · Nice Loops/AICs expert
    Rules out 2 from R9C3.
  16. Step 33 · Cell Forcing Chains expert
    Rules out 8 from R1C1.
  17. Step 35 · XYZ-Wing advanced
    Rules out 6 from R9C6.
  18. Step 36 · XY-Chain expert
    Rules out 2 from R5C3.
  19. Step 38 · Nice Loops/AICs expert
    Rules out 8 from R8C5.
  20. Step 39 · XY-Chain expert
    Rules out 9 from R8C1.
  21. Step 43 · Skyscraper advanced
    Rules out 6 from R9C3.
  22. Step 47 · BUG+1 advanced
    Places 8 in R9C9 and rules out 8 from R7C9, R8C9, R9C1, R9C5.

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.