EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 12: 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 12 of 150 in Extreme Sudoku 3
Difficulty
Expert 6 (expert and beyond), from the opening third of the book
Key technique
Nice Loops/AICs
Hard steps
19 of 44 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 (×3), XY-Chain (×3), WXYZ-Wing (×2), 2-String Kite, Empty Rectangle, Finned Fish, Sue de Coq, X-Wing/Swordfish, XY-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 (19)
  1. Step 9 · 2-String Kite advanced
    Rules out 7 from R7C9.
  2. Step 11 · Empty Rectangle advanced
    Rules out 7 from R4C4.
  3. Step 12 · X-Wing/Swordfish advanced
    Rules out 7 from R5C5.
  4. Step 13 · XYZ-Wing advanced
    Rules out 6 from R4C5.
  5. Step 14 · XY-Chain expert
    Rules out 6 from R4C3.
  6. Step 15 · WXYZ-Wing expert
    Rules out 5 from R7C9.
  7. Step 16 · Sue de Coq expert
    Rules out 8 from R4C5; 6 from R5C5; 5 from R8C4.
  8. Step 17 · ALS-XZ expert
    Rules out 6 from R5C3.
  9. Step 18 · WXYZ-Wing expert
    Rules out 8 from R7C3.
  10. Step 19 · Nice Loops/AICs expert
    Rules out 6 from R4C2.
  11. Step 22 · Finned Fish expert
    Rules out 5 from R9C5.
  12. Step 23 · ALS-XZ expert
    Rules out 5 from R7C7.
  13. Step 24 · ALS-XZ expert
    Rules out 9 from R9C1, R9C3.
  14. Step 26 · XY-Wing advanced
    Rules out 1 from R7C5.
  15. Step 27 · Nice Loops/AICs expert
    Rules out 2 from R7C7.
  16. Step 29 · Nice Loops/AICs expert
    Rules out 6 from R7C7.
  17. Step 31 · Nice Loops/AICs expert
    Rules out 5 from R1C6.
  18. Step 37 · XY-Chain expert
    Rules out 5 from R7C8.
  19. Step 40 · XY-Chain expert
    Rules out 1 from R8C4.

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.