EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 13: 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 13 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
23 of 54 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 (×6), Nice Loops/AICs (×4), XY-Wing (×2), Finned Fish, WXYZ-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 (23)
  1. Step 6 · XY-Chain expert
    Rules out 1 from R8C1.
  2. Step 8 · ALS-XZ expert
    Rules out 1 from R1C1.
  3. Step 9 · ALS-XZ expert
    Rules out 8 from R8C1, R9C4.
  4. Step 11 · ALS-XZ expert
    Rules out 5 from R8C5.
  5. Step 13 · WXYZ-Wing expert
    Rules out 9 from R9C4.
  6. Step 15 · Nice Loops/AICs expert
    Rules out 4 from R4C4.
  7. Step 16 · Nice Loops/AICs expert
    Rules out 9 from R5C4.
  8. Step 18 · XY-Wing advanced
    Rules out 3 from R4C5.
  9. Step 20 · Finned Fish expert
    Rules out 2 from R3C8.
  10. Step 21 · ALS-XZ expert
    Rules out 7 from R5C6.
  11. Step 23 · ALS-XZ expert
    Rules out 1 from R1C6, R5C4.
  12. Step 25 · Nice Loops/AICs expert
    Rules out 1 from R1C4.
  13. Step 26 · ALS-XZ expert
    Rules out 1 from R2C8, R2C9.
  14. Step 29 · ALS-XZ expert
    Rules out 4 from R6C9.
  15. Step 30 · Nice Loops/AICs expert
    Rules out 1 from R3C3.
  16. Step 31 · ALS-XZ expert
    Rules out 2 from R1C1.
  17. Step 32 · ALS-XZ expert
    Rules out 9 from R1C3, R7C1, R8C1.
  18. Step 35 · XY-Chain expert
    Rules out 6 from R1C5.
  19. Step 36 · XY-Chain expert
    Rules out 5 from R7C5.
  20. Step 38 · XY-Chain expert
    Rules out 2 from R7C7.
  21. Step 40 · XY-Wing advanced
    Rules out 4 from R1C9, R3C9.
  22. Step 44 · XY-Chain expert
    Rules out 1 from R3C1.
  23. Step 48 · XY-Chain expert
    Rules out 8 from R7C2, R9C2.

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.