EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 85: 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 85 of 150 in Extreme Sudoku 1
Difficulty
Expert 6 (expert and beyond), from the middle third of the book
Key technique
Nice Loops/AICs
Hard steps
24 of 52 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: Nice Loops/AICs

An alternating chain of strong and weak links. Whichever end is true, the conclusion holds, so the digit at the marked cell is ruled out.

Other advanced and expert techniques in this solve: 2-String Kite (×3), ALS-XZ (×3), Finned Fish (×3), Empty Rectangle (×2), XY-Chain (×2), XY-Wing (×2), Cell Forcing Chains, W-Wing, WXYZ-Wing, 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 (24)
  1. Step 4 · 2-String Kite advanced
    Rules out 2 from R4C4.
  2. Step 5 · Finned Fish expert
    Rules out 1 from R8C2.
  3. Step 6 · Finned Fish expert
    Rules out 2 from R4C5.
  4. Step 9 · Finned Fish expert
    Rules out 6 from R2C3.
  5. Step 10 · ALS-XZ expert
    Rules out 8 from R9C3.
  6. Step 13 · 2-String Kite advanced
    Rules out 8 from R1C2.
  7. Step 14 · Nice Loops/AICs expert
    Rules out 1 from R2C5.
  8. Step 16 · Empty Rectangle advanced
    Rules out 3 from R5C4.
  9. Step 17 · Empty Rectangle advanced
    Rules out 6 from R4C4.
  10. Step 18 · WXYZ-Wing expert
    Rules out 8 from R2C8.
  11. Step 19 · Nice Loops/AICs expert
    Rules out 3 from R5C6.
  12. Step 21 · Nice Loops/AICs expert
    Rules out 3 from R2C5.
  13. Step 22 · Nice Loops/AICs expert
    Rules out 2 from R5C6.
  14. Step 23 · Cell Forcing Chains expert
    Rules out 3 from R1C7.
  15. Step 26 · ALS-XZ expert
    Rules out 6 from R5C3.
  16. Step 27 · Nice Loops/AICs expert
    Rules out 6 from R3C4.
  17. Step 28 · 2-String Kite advanced
    Rules out 6 from R4C1.
  18. Step 30 · XY-Wing advanced
    Rules out 6 from R1C1.
  19. Step 33 · XYZ-Wing advanced
    Rules out 5 from R8C6.
  20. Step 35 · XY-Chain expert
    Rules out 3 from R4C6.
  21. Step 36 · ALS-XZ expert
    Rules out 8 from R7C3.
  22. Step 38 · XY-Chain expert
    Rules out 3 from R8C6.
  23. Step 40 · W-Wing advanced
    Rules out 2 from R4C6, R8C9.
  24. Step 47 · XY-Wing advanced
    Rules out 6 from R8C3.

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.