EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 81: 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 81 of 150 in Extreme Sudoku 2
Difficulty
Expert 7 (expert and beyond), from the middle third of the book
Key technique
Nice Loops/AICs
Hard steps
23 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), Coloring/Multi-coloring (×2), Empty Rectangle (×2), XY-Chain (×2), Cell Forcing Chains, Finned Fish, Skyscraper, W-Wing, WXYZ-Wing, XY-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 (23)
  1. Step 10 · Skyscraper advanced
    Rules out 4 from R3C8.
  2. Step 11 · 2-String Kite advanced
    Rules out 9 from R6C7.
  3. Step 13 · XY-Wing advanced
    Rules out 3 from R5C3.
  4. Step 14 · WXYZ-Wing expert
    Rules out 6 from R8C5.
  5. Step 15 · ALS-XZ expert
    Rules out 7 from R5C2.
  6. Step 16 · Cell Forcing Chains expert
    Rules out 4 from R1C6.
  7. Step 19 · 2-String Kite advanced
    Rules out 4 from R6C8.
  8. Step 20 · 2-String Kite advanced
    Rules out 4 from R6C2.
  9. Step 21 · Empty Rectangle advanced
    Rules out 4 from R8C2.
  10. Step 22 · Finned Fish expert
    Rules out 4 from R5C2.
  11. Step 23 · Coloring/Multi-coloring expert
    Rules out 4 from R8C5.
  12. Step 27 · ALS-XZ expert
    Rules out 1 from R6C9.
  13. Step 28 · Nice Loops/AICs expert
    Rules out 4 from R2C8.
  14. Step 29 · Coloring/Multi-coloring expert
    Rules out 4 from R6C3.
  15. Step 30 · Nice Loops/AICs expert
    Rules out 2 from R5C3.
  16. Step 31 · Nice Loops/AICs expert
    Rules out 8 from R5C8, R5C9.
  17. Step 32 · Nice Loops/AICs expert
    Rules out 7 from R4C5, R5C8, R5C9, R6C5.
  18. Step 33 · Nice Loops/AICs expert
    Rules out 3 from R8C7.
  19. Step 36 · Empty Rectangle advanced
    Rules out 6 from R4C7.
  20. Step 37 · XY-Chain expert
    Rules out 1 from R1C8.
  21. Step 39 · XY-Chain expert
    Rules out 6 from R3C8.
  22. Step 40 · ALS-XZ expert
    Rules out 6 from R3C9.
  23. Step 47 · W-Wing advanced
    Rules out 6 from R9C1.

The book

Volume two: 150 new classic 9×9 grids, none repeated from book 1, 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.

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