EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 108: 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 108 of 150 in Extreme Sudoku 3
Difficulty
Expert 6 (expert and beyond), from the final, hardest third of the book
Key technique
Nice Loops/AICs
Hard steps
22 of 40 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), Empty Rectangle (×3), W-Wing (×2), XY-Wing (×2), 2-String Kite, Cell Forcing Chains, Finned Fish, WXYZ-Wing, XY-Chain.

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 4 · 2-String Kite advanced
    Rules out 1 from R6C2.
  2. Step 5 · Empty Rectangle advanced
    Rules out 9 from R8C6.
  3. Step 6 · Finned Fish expert
    Rules out 1 from R3C1.
  4. Step 7 · Nice Loops/AICs expert
    Rules out 5 from R6C6.
  5. Step 9 · W-Wing advanced
    Rules out 1 from R6C9.
  6. Step 10 · ALS-XZ expert
    Rules out 5 from R8C4.
  7. Step 11 · Nice Loops/AICs expert
    Rules out 9 from R4C9.
  8. Step 12 · Cell Forcing Chains expert
    Rules out 8 from R3C7.
  9. Step 14 · ALS-XZ expert
    Rules out 8 from R4C8, R4C9.
  10. Step 15 · ALS-XZ expert
    Rules out 3 from R6C1.
  11. Step 16 · ALS-XZ expert
    Rules out 8 from R6C8.
  12. Step 17 · ALS-XZ expert
    Rules out 2 from R7C9.
  13. Step 18 · Empty Rectangle advanced
    Rules out 2 from R1C4.
  14. Step 19 · Nice Loops/AICs expert
    Rules out 2 from R1C3.
  15. Step 20 · Empty Rectangle advanced
    Rules out 2 from R9C9.
  16. Step 21 · W-Wing advanced
    Rules out 4 from R2C3, R3C8.
  17. Step 23 · Nice Loops/AICs expert
    Rules out 1 from R1C2.
  18. Step 24 · Nice Loops/AICs expert
    Rules out 8 from R1C9.
  19. Step 27 · WXYZ-Wing expert
    Rules out 9 from R5C9.
  20. Step 33 · XY-Wing advanced
    Rules out 5 from R9C4.
  21. Step 35 · XY-Chain expert
    Rules out 7 from R9C5.
  22. Step 36 · XY-Wing advanced
    Rules out 9 from R4C5.

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.