EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 7: 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 7 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
21 of 47 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), XY-Wing (×2), XYZ-Wing (×2), 2-String Kite, Finned Fish, Nice Loops/AICs, Skyscraper, W-Wing, 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 (21)
  1. Step 3 · Skyscraper advanced
    Rules out 3 from R4C7, R4C9, R6C1.
  2. Step 8 · XY-Wing advanced
    Rules out 4 from R3C2.
  3. Step 10 · XY-Chain expert
    Rules out 3 from R9C9.
  4. Step 11 · XY-Chain expert
    Rules out 3 from R6C9.
  5. Step 12 · ALS-XZ expert
    Rules out 4 from R1C3.
  6. Step 13 · ALS-XZ expert
    Rules out 9 from R5C1.
  7. Step 14 · XYZ-Wing advanced
    Rules out 7 from R6C3.
  8. Step 16 · ALS-XZ expert
    Rules out 1 from R8C5.
  9. Step 17 · ALS-XZ expert
    Rules out 4 from R3C7.
  10. Step 18 · ALS-XZ expert
    Rules out 7 from R1C3.
  11. Step 22 · XYZ-Wing advanced
    Rules out 7 from R3C5.
  12. Step 23 · WXYZ-Wing expert
    Rules out 7 from R5C5.
  13. Step 24 · Nice Loops/AICs expert
    Rules out 4 from R1C9.
  14. Step 27 · Finned Fish expert
    Rules out 9 from R6C6.
  15. Step 29 · XY-Chain expert
    Rules out 4 from R3C9.
  16. Step 30 · XY-Chain expert
    Rules out 4 from R7C7, R9C7.
  17. Step 31 · XY-Chain expert
    Rules out 7 from R2C5.
  18. Step 34 · W-Wing advanced
    Rules out 8 from R9C7.
  19. Step 36 · 2-String Kite advanced
    Rules out 8 from R4C9.
  20. Step 37 · XY-Chain expert
    Rules out 9 from R8C6.
  21. Step 40 · XY-Wing advanced
    Rules out 9 from R4C5.

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.