EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 20: 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 20 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
19 of 38 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 (×5), XY-Chain (×2), Cell Forcing Chains, Empty Rectangle, Finned Fish, XY-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 (19)
  1. Step 5 · Empty Rectangle advanced
    Rules out 2 from R4C3.
  2. Step 6 · ALS-XZ expert
    Rules out 9 from R1C4.
  3. Step 8 · ALS-XZ expert
    Rules out 3 from R7C6.
  4. Step 9 · ALS-XZ expert
    Rules out 2 from R7C6.
  5. Step 11 · ALS-XZ expert
    Rules out 5 from R4C4, R5C4.
  6. Step 12 · ALS-XZ expert
    Rules out 5 from R4C6.
  7. Step 13 · ALS-XZ expert
    Rules out 8 from R5C2.
  8. Step 14 · Nice Loops/AICs expert
    Rules out 9 from R1C2.
  9. Step 15 · Nice Loops/AICs expert
    Rules out 9 from R1C7.
  10. Step 16 · Nice Loops/AICs expert
    Rules out 3 from R1C2.
  11. Step 17 · Nice Loops/AICs expert
    Rules out 3 from R9C7.
  12. Step 18 · Nice Loops/AICs expert
    Rules out 3 from R5C2.
  13. Step 19 · Cell Forcing Chains expert
    Rules out 1 from R1C6.
  14. Step 23 · XY-Wing advanced
    Rules out 7 from R3C2, R4C3.
  15. Step 24 · XY-Chain expert
    Rules out 3 from R4C2.
  16. Step 25 · XY-Chain expert
    Rules out 8 from R3C3, R4C2.
  17. Step 27 · ALS-XZ expert
    Rules out 3 from R1C3.
  18. Step 30 · Finned Fish expert
    Rules out 3 from R9C1.
  19. Step 32 · ALS-XZ expert
    Rules out 1 from R4C6, R6C8.

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.