EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 77: 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 77 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
20 of 44 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 (×3), WXYZ-Wing (×2), 2-String Kite, Cell Forcing Chains, Empty Rectangle, Finned Fish, Skyscraper, Sue de Coq, 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 (20)
  1. Step 3 · 2-String Kite advanced
    Rules out 2 from R9C7.
  2. Step 4 · Sue de Coq expert
    Rules out 1 from R7C9; 2 from R7C9, R9C9; 6 from R8C3.
  3. Step 5 · ALS-XZ expert
    Rules out 2 from R1C8.
  4. Step 6 · XYZ-Wing advanced
    Rules out 6 from R1C3.
  5. Step 7 · ALS-XZ expert
    Rules out 5 from R9C6.
  6. Step 9 · Nice Loops/AICs expert
    Rules out 2 from R3C6.
  7. Step 11 · Nice Loops/AICs expert
    Rules out 4 from R1C5.
  8. Step 13 · Nice Loops/AICs expert
    Rules out 9 from R4C7.
  9. Step 14 · ALS-XZ expert
    Rules out 9 from R3C6.
  10. Step 15 · Nice Loops/AICs expert
    Rules out 7 from R1C9.
  11. Step 16 · Cell Forcing Chains expert
    Rules out 9 from R1C9.
  12. Step 20 · Empty Rectangle advanced
    Rules out 6 from R2C7.
  13. Step 21 · WXYZ-Wing expert
    Rules out 6 from R1C4, R1C5.
  14. Step 22 · Skyscraper advanced
    Rules out 6 from R3C7, R8C8.
  15. Step 23 · WXYZ-Wing expert
    Rules out 9 from R2C7.
  16. Step 24 · ALS-XZ expert
    Rules out 6 from R3C4.
  17. Step 33 · Finned Fish expert
    Rules out 3 from R4C1.
  18. Step 34 · XY-Chain expert
    Rules out 7 from R6C2.
  19. Step 36 · XY-Chain expert
    Rules out 7 from R4C3, R6C3.
  20. Step 41 · XY-Chain expert
    Rules out 2 from R1C5.

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.