EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, 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 3
Difficulty
Expert 7 (expert and beyond), from the middle third of the book
Key technique
Nice Loops/AICs
Hard steps
28 of 51 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: ALS-XZ (×5), 2-String Kite (×2), XY-Wing (×2), Cell Forcing Chains, Empty Rectangle, Finned Fish, Sue de Coq, WXYZ-Wing, XY-Chain, 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 of 28)
  1. Step 4 · 2-String Kite advanced
    Rules out 9 from R3C8.
  2. Step 6 · Empty Rectangle advanced
    Rules out 6 from R5C8.
  3. Step 7 · Finned Fish expert
    Rules out 4 from R4C4, R6C4.
  4. Step 8 · ALS-XZ expert
    Rules out 5 from R8C8, R9C4.
  5. Step 10 · ALS-XZ expert
    Rules out 5 from R3C8.
  6. Step 11 · ALS-XZ expert
    Rules out 1 from R7C4.
  7. Step 12 · ALS-XZ expert
    Rules out 7 from R4C7, R5C7.
  8. Step 13 · Nice Loops/AICs expert
    Rules out 8 from R1C3.
  9. Step 14 · Nice Loops/AICs expert
    Rules out 9 from R2C7.
  10. Step 15 · WXYZ-Wing expert
    Rules out 3 from R1C7.
  11. Step 16 · XY-Wing advanced
    Rules out 9 from R1C1.
  12. Step 18 · Nice Loops/AICs expert
    Rules out 6 from R4C5, R5C5.
  13. Step 19 · Nice Loops/AICs expert
    Rules out 7 from R4C8.
  14. Step 20 · Nice Loops/AICs expert
    Rules out 7 from R6C8.
  15. Step 21 · Nice Loops/AICs expert
    Rules out 5 from R4C8.
  16. Step 22 · Nice Loops/AICs expert
    Rules out 5 from R6C8.
  17. Step 23 · Nice Loops/AICs expert
    Rules out 6 from R7C6.
  18. Step 27 · ALS-XZ expert
    Rules out 4 from R6C1.
  19. Step 28 · Cell Forcing Chains expert
    Rules out 3 from R1C1.
  20. Step 30 · 2-String Kite advanced
    Rules out 3 from R4C3.
  21. Step 31 · Nice Loops/AICs expert
    Rules out 1 from R4C2.
  22. Step 32 · Nice Loops/AICs expert
    Rules out 7 from R4C5.
  23. Step 33 · Sue de Coq expert
    Rules out 5 from R5C2, R5C7.
  24. Step 36 · Nice Loops/AICs expert
    Rules out 5 from R6C9.

The book

Volume three: 150 new classic 9×9 grids, none repeated from books 1 or 2, ramping from hard to brutal.

150 new 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.

On Amazon from 8 Dec About the book

Try a free sample puzzle (PDF) · prints on A4 or US Letter

More step-by-step solutions: Extreme Sudoku 1 · Extreme Killer Sudoku 1 · Extreme Sudoku 2 · Extreme Killer Sudoku 2 · Extreme Killer Sudoku 3.