EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 21: 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 21 of 150 in Extreme Sudoku 2
Difficulty
Expert 5 (expert and beyond), from the opening third of the book
Key technique
ALS-XZ
Hard steps
19 of 47 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 (×2), Cell Forcing Chains, Finned Fish, Skyscraper, W-Wing, X-Wing/Swordfish.

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 6 · X-Wing/Swordfish advanced
    Rules out 2 from R3C1, R3C5, R4C1, R8C1 and 1 more.
  2. Step 7 · Finned Fish expert
    Rules out 9 from R2C8, R3C8.
  3. Step 8 · ALS-XZ expert
    Rules out 7 from R4C3.
  4. Step 9 · Nice Loops/AICs expert
    Rules out 1 from R1C9.
  5. Step 10 · Nice Loops/AICs expert
    Rules out 7 from R3C2.
  6. Step 11 · Nice Loops/AICs expert
    Rules out 6 from R3C2.
  7. Step 12 · Cell Forcing Chains expert
    Rules out 9 from R1C8.
  8. Step 15 · ALS-XZ expert
    Rules out 9 from R7C5.
  9. Step 21 · W-Wing advanced
    Rules out 4 from R2C3.
  10. Step 22 · ALS-XZ expert
    Rules out 2 from R3C3.
  11. Step 24 · ALS-XZ expert
    Rules out 6 from R8C3.
  12. Step 25 · ALS-XZ expert
    Rules out 2 from R8C3.
  13. Step 26 · ALS-XZ expert
    Rules out 5 from R8C8.
  14. Step 27 · ALS-XZ expert
    Rules out 3 from R8C3.
  15. Step 30 · ALS-XZ expert
    Rules out 6 from R1C1.
  16. Step 32 · XY-Chain expert
    Rules out 3 from R7C5, R8C8, R8C9.
  17. Step 33 · ALS-XZ expert
    Rules out 7 from R3C6.
  18. Step 36 · XY-Chain expert
    Rules out 5 from R9C8.
  19. Step 42 · Skyscraper advanced
    Rules out 3 from R4C8, R7C9.

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.