EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 45: 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 45 of 150 in Extreme Sudoku 1
Difficulty
Expert 5 (expert and beyond), from the opening third of the book
Key technique
ALS-XZ
Hard steps
22 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 (×4), 2-String Kite (×3), Skyscraper (×2), Cell Forcing Chains, Empty Rectangle, W-Wing, WXYZ-Wing, XY-Chain.

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 5 · 2-String Kite advanced
    Rules out 2 from R5C4.
  2. Step 6 · Nice Loops/AICs expert
    Rules out 6 from R7C2.
  3. Step 7 · ALS-XZ expert
    Rules out 6 from R5C3.
  4. Step 8 · Nice Loops/AICs expert
    Rules out 6 from R3C5.
  5. Step 9 · Nice Loops/AICs expert
    Rules out 6 from R3C2.
  6. Step 10 · Nice Loops/AICs expert
    Rules out 3 from R8C6.
  7. Step 11 · Cell Forcing Chains expert
    Rules out 6 from R2C1.
  8. Step 14 · 2-String Kite advanced
    Rules out 5 from R5C6.
  9. Step 15 · ALS-XZ expert
    Rules out 6 from R4C1.
  10. Step 16 · ALS-XZ expert
    Rules out 7 from R4C1.
  11. Step 18 · ALS-XZ expert
    Rules out 6 from R4C3.
  12. Step 19 · ALS-XZ expert
    Rules out 3 from R7C4.
  13. Step 20 · Skyscraper advanced
    Rules out 3 from R9C3.
  14. Step 25 · WXYZ-Wing expert
    Rules out 6 from R2C4.
  15. Step 27 · Empty Rectangle advanced
    Rules out 6 from R5C6.
  16. Step 28 · ALS-XZ expert
    Rules out 7 from R3C2.
  17. Step 33 · 2-String Kite advanced
    Rules out 6 from R5C4.
  18. Step 34 · ALS-XZ expert
    Rules out 7 from R6C6.
  19. Step 35 · ALS-XZ expert
    Rules out 9 from R9C6.
  20. Step 37 · XY-Chain expert
    Rules out 9 from R3C5, R8C6.
  21. Step 42 · Skyscraper advanced
    Rules out 6 from R4C5, R6C9.
  22. Step 43 · W-Wing advanced
    Rules out 6 from R3C4.

The book

Classic 9×9 sudoku with the warm-up taken out. Every grid sits at the top of the expert range or beyond it, and the book ramps from hard to brutal.

150 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 Killer Sudoku 1 · Extreme Sudoku 2 · Extreme Killer Sudoku 2 · Extreme Sudoku 3 · Extreme Killer Sudoku 3.