EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 72: 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 72 of 150 in Extreme Sudoku 1
Difficulty
Expert 5 (expert and beyond), from the middle third of the book
Key technique
ALS-XZ
Hard steps
20 of 44 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 (×4), Finned Fish (×3), Nice Loops/AICs (×2), W-Wing (×2), Empty Rectangle, Skyscraper, WXYZ-Wing, X-Wing/Swordfish, 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 (20)
  1. Step 8 · Empty Rectangle advanced
    Rules out 1 from R9C1.
  2. Step 9 · Finned Fish expert
    Rules out 3 from R8C7.
  3. Step 12 · X-Wing/Swordfish advanced
    Rules out 1 from R1C6, R5C6.
  4. Step 13 · WXYZ-Wing expert
    Rules out 5 from R5C4, R5C6.
  5. Step 14 · W-Wing advanced
    Rules out 2 from R1C6.
  6. Step 16 · ALS-XZ expert
    Rules out 2 from R3C3.
  7. Step 17 · ALS-XZ expert
    Rules out 2 from R1C4, R3C2.
  8. Step 19 · ALS-XZ expert
    Rules out 5 from R6C2.
  9. Step 21 · Nice Loops/AICs expert
    Rules out 9 from R7C3.
  10. Step 22 · ALS-XZ expert
    Rules out 5 from R8C1.
  11. Step 23 · Nice Loops/AICs expert
    Rules out 1 from R3C5.
  12. Step 24 · W-Wing advanced
    Rules out 4 from R5C1.
  13. Step 27 · Skyscraper advanced
    Rules out 5 from R4C6, R7C4, R9C4.
  14. Step 28 · Finned Fish expert
    Rules out 5 from R7C1.
  15. Step 29 · XY-Chain expert
    Rules out 2 from R1C3.
  16. Step 34 · XY-Chain expert
    Rules out 7 from R8C6.
  17. Step 36 · XYZ-Wing advanced
    Rules out 7 from R9C4.
  18. Step 37 · XY-Chain expert
    Rules out 9 from R9C1.
  19. Step 38 · Finned Fish expert
    Rules out 9 from R7C7.
  20. Step 40 · XY-Chain expert
    Rules out 3 from R1C7, R3C5.

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.