EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 108: 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 108 of 150 in Extreme Sudoku 1
Difficulty
Expert 5 (expert and beyond), from the final, hardest third of the book
Key technique
ALS-XZ
Hard steps
17 of 42 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 (×2), Skyscraper (×2), W-Wing (×2), 2-String Kite, Cell Forcing Chains, WXYZ-Wing, X-Wing/Swordfish, XY-Chain, 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 (17)
  1. Step 3 · Skyscraper advanced
    Rules out 8 from R3C3, R8C1.
  2. Step 6 · 2-String Kite advanced
    Rules out 9 from R7C5.
  3. Step 7 · W-Wing advanced
    Rules out 6 from R8C6.
  4. Step 8 · ALS-XZ expert
    Rules out 6 from R4C7.
  5. Step 9 · ALS-XZ expert
    Rules out 3 from R2C8.
  6. Step 15 · ALS-XZ expert
    Rules out 2 from R9C4.
  7. Step 18 · Nice Loops/AICs expert
    Rules out 2 from R8C6.
  8. Step 19 · Nice Loops/AICs expert
    Rules out 4 from R8C7.
  9. Step 21 · ALS-XZ expert
    Rules out 3 from R1C5.
  10. Step 22 · Cell Forcing Chains expert
    Rules out 3 from R1C2.
  11. Step 25 · XYZ-Wing advanced
    Rules out 6 from R9C8.
  12. Step 26 · WXYZ-Wing expert
    Rules out 6 from R7C5.
  13. Step 29 · XY-Wing advanced
    Rules out 2 from R8C9.
  14. Step 33 · X-Wing/Swordfish advanced
    Rules out 9 from R9C4.
  15. Step 35 · Skyscraper advanced
    Rules out 7 from R4C7, R8C8.
  16. Step 36 · W-Wing advanced
    Rules out 3 from R3C4, R6C6.
  17. Step 38 · XY-Chain expert
    Rules out 9 from R1C8, R9C5.

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.