EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 32: 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 32 of 150 in Extreme Sudoku 1
Difficulty
Expert 5 (expert and beyond), from the opening third of the book
Key technique
XY-Chain
Hard steps
23 of 48 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: XY-Chain

A chain of two-candidate cells, each linked to the next. Whichever way the start cell goes, one end of the chain holds the digit, so cells seeing both ends cannot.

Other advanced and expert techniques in this solve: ALS-XZ (×5), Nice Loops/AICs (×4), Skyscraper (×3), WXYZ-Wing (×3), Empty Rectangle, Finned Fish.

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 4 · Empty Rectangle advanced
    Rules out 3 from R6C3.
  2. Step 5 · WXYZ-Wing expert
    Rules out 6 from R8C6.
  3. Step 6 · ALS-XZ expert
    Rules out 7 from R2C5.
  4. Step 7 · Nice Loops/AICs expert
    Rules out 4 from R1C1.
  5. Step 8 · Nice Loops/AICs expert
    Rules out 3 from R7C5, R9C1.
  6. Step 11 · ALS-XZ expert
    Rules out 9 from R8C6.
  7. Step 12 · Nice Loops/AICs expert
    Rules out 4 from R2C5.
  8. Step 13 · Nice Loops/AICs expert
    Rules out 9 from R3C1.
  9. Step 17 · WXYZ-Wing expert
    Rules out 4 from R6C9.
  10. Step 18 · Skyscraper advanced
    Rules out 4 from R1C3, R4C2.
  11. Step 20 · Skyscraper advanced
    Rules out 7 from R4C5, R4C6, R6C1.
  12. Step 21 · WXYZ-Wing expert
    Rules out 6 from R6C6.
  13. Step 22 · ALS-XZ expert
    Rules out 6 from R6C4.
  14. Step 24 · XY-Chain expert
    Rules out 1 from R6C3.
  15. Step 26 · XY-Chain expert
    Rules out 9 from R5C5, R6C1.
  16. Step 30 · Finned Fish expert
    Rules out 2 from R7C8, R7C9.
  17. Step 31 · ALS-XZ expert
    Rules out 7 from R1C6.
  18. Step 32 · ALS-XZ expert
    Rules out 2 from R7C7.
  19. Step 35 · XY-Chain expert
    Rules out 2 from R9C8.
  20. Step 37 · XY-Chain expert
    Rules out 7 from R3C9.
  21. Step 38 · XY-Chain expert
    Rules out 7 from R7C8, R8C8.
  22. Step 39 · XY-Chain expert
    Rules out 5 from R7C6, R8C8.
  23. Step 42 · Skyscraper advanced
    Rules out 7 from R3C4.

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.