EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 131: 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 131 of 150 in Extreme Sudoku 3
Difficulty
Expert 7 (expert and beyond), from the final, hardest third of the book
Key technique
ALS-XZ
Hard steps
18 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: ALS-XZ

Two almost-locked sets (n cells with n+1 candidates) share a restricted digit X. Then a digit Z common to both must be in one of them, so cells seeing all of its copies cannot be Z.

Other advanced and expert techniques in this solve: 2-String Kite (×3), Nice Loops/AICs (×3), Finned Fish (×2), WXYZ-Wing (×2), Cell Forcing Chains, Empty Rectangle, Sue de Coq, 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 (18)
  1. Step 8 · 2-String Kite advanced
    Rules out 3 from R5C8.
  2. Step 9 · 2-String Kite advanced
    Rules out 5 from R3C2.
  3. Step 11 · Finned Fish expert
    Rules out 3 from R5C7.
  4. Step 12 · WXYZ-Wing expert
    Rules out 8 from R7C4.
  5. Step 13 · ALS-XZ expert
    Rules out 8 from R5C1.
  6. Step 14 · ALS-XZ expert
    Rules out 7 from R1C2.
  7. Step 15 · ALS-XZ expert
    Rules out 1 from R1C5, R1C6, R2C2.
  8. Step 18 · Cell Forcing Chains expert
    Rules out 9 from R1C4.
  9. Step 21 · ALS-XZ expert
    Rules out 6 from R4C8.
  10. Step 23 · Nice Loops/AICs expert
    Rules out 7 from R2C2.
  11. Step 24 · WXYZ-Wing expert
    Rules out 8 from R1C1.
  12. Step 25 · Sue de Coq expert
    Rules out 8 from R3C8.
  13. Step 26 · Nice Loops/AICs expert
    Rules out 2 from R1C9.
  14. Step 28 · Nice Loops/AICs expert
    Rules out 5 from R3C6, R4C4.
  15. Step 30 · 2-String Kite advanced
    Rules out 8 from R4C1.
  16. Step 35 · XY-Chain expert
    Rules out 8 from R1C8, R6C7.
  17. Step 41 · Empty Rectangle advanced
    Rules out 8 from R3C2.
  18. Step 42 · Finned Fish expert
    Rules out 8 from R9C5.

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.