EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, 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 3
Difficulty
Expert 5 (expert and beyond), from the middle third of the book
Key technique
Nice Loops/AICs
Hard steps
22 of 49 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), XY-Chain (×4), 2-String Kite, Cell Forcing Chains, Empty Rectangle, Finned Fish, X-Wing/Swordfish, 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 (22)
  1. Step 7 · Finned Fish expert
    Rules out 6 from R2C7.
  2. Step 9 · 2-String Kite advanced
    Rules out 3 from R7C5.
  3. Step 10 · Empty Rectangle advanced
    Rules out 3 from R7C3.
  4. Step 12 · ALS-XZ expert
    Rules out 2 from R6C1.
  5. Step 13 · ALS-XZ expert
    Rules out 5 from R6C3.
  6. Step 14 · Nice Loops/AICs expert
    Rules out 6 from R3C5.
  7. Step 15 · Nice Loops/AICs expert
    Rules out 6 from R1C5.
  8. Step 16 · Nice Loops/AICs expert
    Rules out 9 from R1C8.
  9. Step 17 · Nice Loops/AICs expert
    Rules out 5 from R7C3.
  10. Step 18 · Cell Forcing Chains expert
    Rules out 5 from R1C5.
  11. Step 20 · ALS-XZ expert
    Rules out 9 from R2C8.
  12. Step 21 · Nice Loops/AICs expert
    Rules out 3 from R2C9.
  13. Step 22 · Nice Loops/AICs expert
    Rules out 3 from R2C8.
  14. Step 25 · ALS-XZ expert
    Rules out 2 from R6C9.
  15. Step 26 · Nice Loops/AICs expert
    Rules out 3 from R9C3.
  16. Step 27 · ALS-XZ expert
    Rules out 6 from R7C5.
  17. Step 31 · XY-Chain expert
    Rules out 9 from R2C9, R7C8.
  18. Step 37 · XY-Chain expert
    Rules out 5 from R8C4.
  19. Step 38 · XY-Chain expert
    Rules out 6 from R1C9.
  20. Step 39 · X-Wing/Swordfish advanced
    Rules out 6 from R6C7.
  21. Step 41 · XY-Wing advanced
    Rules out 1 from R1C3, R4C2.
  22. Step 42 · XY-Chain expert
    Rules out 5 from R9C4.

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.