EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 136: 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 136 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
21 of 46 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: XY-Chain (×4), Nice Loops/AICs (×2), W-Wing (×2), XY-Wing (×2), 2-String Kite, Cell Forcing Chains, Empty Rectangle, Finned Fish, Sue de Coq, WXYZ-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 (21)
  1. Step 4 · 2-String Kite advanced
    Rules out 5 from R5C7.
  2. Step 5 · Empty Rectangle advanced
    Rules out 7 from R5C7.
  3. Step 6 · XY-Wing advanced
    Rules out 7 from R5C5.
  4. Step 7 · XY-Wing advanced
    Rules out 6 from R1C5, R3C5.
  5. Step 8 · Finned Fish expert
    Rules out 5 from R6C7.
  6. Step 9 · ALS-XZ expert
    Rules out 4 from R2C1.
  7. Step 10 · ALS-XZ expert
    Rules out 7 from R2C1, R5C2.
  8. Step 11 · Nice Loops/AICs expert
    Rules out 5 from R5C5.
  9. Step 15 · XY-Chain expert
    Rules out 4 from R1C3.
  10. Step 16 · ALS-XZ expert
    Rules out 4 from R4C7, R4C8.
  11. Step 18 · W-Wing advanced
    Rules out 7 from R4C3.
  12. Step 20 · XY-Chain expert
    Rules out 5 from R3C8.
  13. Step 21 · ALS-XZ expert
    Rules out 5 from R2C8.
  14. Step 22 · Cell Forcing Chains expert
    Rules out 2 from R1C5.
  15. Step 26 · W-Wing advanced
    Rules out 7 from R1C8, R1C9, R2C2.
  16. Step 27 · XY-Chain expert
    Rules out 7 from R1C3, R8C2.
  17. Step 29 · Sue de Coq expert
    Rules out 6 from R2C9, R3C9; 9 from R3C9; 5 from R4C7.
  18. Step 32 · WXYZ-Wing expert
    Rules out 6 from R1C3.
  19. Step 34 · Nice Loops/AICs expert
    Rules out 4 from R1C8.
  20. Step 36 · ALS-XZ expert
    Rules out 9 from R9C8.
  21. Step 41 · XY-Chain expert
    Rules out 9 from R1C9.

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.