EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 135: 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 135 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
25 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), XY-Chain (×4), 2-String Kite (×3), W-Wing (×2), WXYZ-Wing (×2), Cell Forcing Chains, Coloring/Multi-coloring, Finned Fish, 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 (24 of 25)
  1. Step 5 · 2-String Kite advanced
    Rules out 6 from R5C5.
  2. Step 6 · 2-String Kite advanced
    Rules out 9 from R3C7.
  3. Step 7 · WXYZ-Wing expert
    Rules out 3 from R6C4.
  4. Step 8 · WXYZ-Wing expert
    Rules out 3 from R5C4, R7C6, R8C6.
  5. Step 10 · Coloring/Multi-coloring expert
    Rules out 6 from R3C4.
  6. Step 11 · ALS-XZ expert
    Rules out 9 from R6C6.
  7. Step 12 · Nice Loops/AICs expert
    Rules out 4 from R2C5.
  8. Step 13 · Nice Loops/AICs expert
    Rules out 3 from R6C6.
  9. Step 14 · W-Wing advanced
    Rules out 2 from R6C3, R8C6.
  10. Step 15 · Nice Loops/AICs expert
    Rules out 2 from R7C7.
  11. Step 16 · Cell Forcing Chains expert
    Rules out 2 from R1C3.
  12. Step 18 · 2-String Kite advanced
    Rules out 3 from R2C7.
  13. Step 19 · XY-Wing advanced
    Rules out 9 from R1C6, R3C8, R3C9.
  14. Step 20 · Finned Fish expert
    Rules out 3 from R2C9.
  15. Step 21 · ALS-XZ expert
    Rules out 4 from R1C2.
  16. Step 22 · ALS-XZ expert
    Rules out 7 from R1C1.
  17. Step 23 · Nice Loops/AICs expert
    Rules out 2 from R6C1.
  18. Step 25 · XY-Chain expert
    Rules out 9 from R9C8.
  19. Step 27 · Nice Loops/AICs expert
    Rules out 2 from R8C1.
  20. Step 29 · Nice Loops/AICs expert
    Rules out 4 from R8C1.
  21. Step 33 · XY-Chain expert
    Rules out 2 from R5C4.
  22. Step 36 · ALS-XZ expert
    Rules out 3 from R5C9.
  23. Step 39 · W-Wing advanced
    Rules out 1 from R1C7, R1C8, R2C5, R2C6.
  24. Step 42 · XY-Chain expert
    Rules out 5 from R1C7.

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.