EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 66: 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 66 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
18 of 41 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 (×3), XY-Chain (×3), Empty Rectangle (×2), Cell Forcing Chains, Finned Fish, W-Wing, WXYZ-Wing, 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 (18)
  1. Step 6 · Empty Rectangle advanced
    Rules out 2 from R6C6.
  2. Step 7 · XYZ-Wing advanced
    Rules out 2 from R8C9.
  3. Step 8 · Empty Rectangle advanced
    Rules out 2 from R2C8.
  4. Step 9 · Finned Fish expert
    Rules out 2 from R2C9.
  5. Step 10 · WXYZ-Wing expert
    Rules out 2 from R9C7.
  6. Step 12 · ALS-XZ expert
    Rules out 1 from R2C2, R3C7, R3C9.
  7. Step 14 · W-Wing advanced
    Rules out 4 from R2C9, R3C6.
  8. Step 16 · ALS-XZ expert
    Rules out 5 from R6C1.
  9. Step 17 · Nice Loops/AICs expert
    Rules out 1 from R5C2.
  10. Step 19 · Cell Forcing Chains expert
    Rules out 1 from R1C3.
  11. Step 22 · ALS-XZ expert
    Rules out 9 from R4C4.
  12. Step 23 · Nice Loops/AICs expert
    Rules out 9 from R9C7.
  13. Step 25 · Nice Loops/AICs expert
    Rules out 1 from R6C8.
  14. Step 29 · XY-Chain expert
    Rules out 1 from R5C6.
  15. Step 30 · ALS-XZ expert
    Rules out 1 from R6C6.
  16. Step 35 · XY-Chain expert
    Rules out 2 from R6C4.
  17. Step 36 · XY-Wing advanced
    Rules out 5 from R4C4.
  18. Step 37 · XY-Chain expert
    Rules out 2 from R1C5, R4C4.

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.