EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 116: 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 116 of 150 in Extreme Sudoku 3
Difficulty
Expert 7 (expert and beyond), from the final, hardest third of the book
Key technique
Nice Loops/AICs
Hard steps
24 of 47 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 (×4), Finned Fish (×2), Skyscraper (×2), Cell Forcing Chains, Empty Rectangle, Sue de Coq, 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 (24)
  1. Step 3 · Finned Fish expert
    Rules out 9 from R2C6.
  2. Step 4 · Nice Loops/AICs expert
    Rules out 6 from R7C1.
  3. Step 5 · Nice Loops/AICs expert
    Rules out 6 from R8C1.
  4. Step 6 · Nice Loops/AICs expert
    Rules out 4 from R2C4.
  5. Step 7 · Nice Loops/AICs expert
    Rules out 2 from R2C9.
  6. Step 11 · Nice Loops/AICs expert
    Rules out 5 from R1C1.
  7. Step 12 · Empty Rectangle advanced
    Rules out 5 from R3C5.
  8. Step 13 · Cell Forcing Chains expert
    Rules out 6 from R2C4.
  9. Step 15 · Finned Fish expert
    Rules out 6 from R7C7, R7C9.
  10. Step 16 · Nice Loops/AICs expert
    Rules out 9 from R3C3.
  11. Step 17 · ALS-XZ expert
    Rules out 5 from R1C2.
  12. Step 19 · ALS-XZ expert
    Rules out 8 from R4C6.
  13. Step 20 · Nice Loops/AICs expert
    Rules out 7 from R1C8.
  14. Step 23 · Skyscraper advanced
    Rules out 6 from R8C5.
  15. Step 27 · WXYZ-Wing expert
    Rules out 8 from R1C5.
  16. Step 28 · ALS-XZ expert
    Rules out 9 from R2C5, R3C1.
  17. Step 29 · Nice Loops/AICs expert
    Rules out 8 from R8C2.
  18. Step 30 · Sue de Coq expert
    Rules out 8 from R4C1; 9 from R4C1.
  19. Step 31 · Nice Loops/AICs expert
    Rules out 9 from R5C2.
  20. Step 32 · Nice Loops/AICs expert
    Rules out 4 from R8C6.
  21. Step 33 · ALS-XZ expert
    Rules out 2 from R7C6, R8C7.
  22. Step 35 · Nice Loops/AICs expert
    Rules out 9 from R4C2.
  23. Step 40 · XY-Chain expert
    Rules out 3 from R5C4.
  24. Step 44 · Skyscraper advanced
    Rules out 3 from R4C1, R8C2.

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.