EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 27: 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 27 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 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: XY-Chain (×5), Nice Loops/AICs (×4), Finned Fish (×2), 2-String Kite, W-Wing, WXYZ-Wing, X-Wing/Swordfish, 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 (22)
  1. Step 4 · Finned Fish expert
    Rules out 6 from R6C4.
  2. Step 5 · ALS-XZ expert
    Rules out 1 from R8C1.
  3. Step 7 · 2-String Kite advanced
    Rules out 9 from R2C6.
  4. Step 8 · XY-Wing advanced
    Rules out 9 from R2C9.
  5. Step 10 · Nice Loops/AICs expert
    Rules out 6 from R5C7.
  6. Step 11 · WXYZ-Wing expert
    Rules out 2 from R6C9.
  7. Step 12 · ALS-XZ expert
    Rules out 2 from R2C7.
  8. Step 13 · Nice Loops/AICs expert
    Rules out 6 from R4C6.
  9. Step 14 · Nice Loops/AICs expert
    Rules out 9 from R2C5.
  10. Step 15 · Nice Loops/AICs expert
    Rules out 4 from R4C8.
  11. Step 16 · W-Wing advanced
    Rules out 3 from R2C9, R7C7, R8C7.
  12. Step 17 · ALS-XZ expert
    Rules out 2 from R4C9.
  13. Step 18 · XY-Chain expert
    Rules out 2 from R8C7.
  14. Step 21 · XY-Chain expert
    Rules out 3 from R3C4.
  15. Step 23 · ALS-XZ expert
    Rules out 6 from R4C5.
  16. Step 24 · X-Wing/Swordfish advanced
    Rules out 6 from R8C4.
  17. Step 26 · ALS-XZ expert
    Rules out 1 from R8C7.
  18. Step 32 · XY-Chain expert
    Rules out 4 from R6C1.
  19. Step 33 · XY-Chain expert
    Rules out 5 from R1C3.
  20. Step 34 · Finned Fish expert
    Rules out 5 from R6C1.
  21. Step 35 · XYZ-Wing advanced
    Rules out 6 from R6C5.
  22. Step 37 · XY-Chain expert
    Rules out 4 from R7C1.

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.