EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 133: 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 133 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
23 of 50 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: Nice Loops/AICs (×5), XY-Chain (×4), 2-String Kite, Cell Forcing Chains, Coloring/Multi-coloring, Empty Rectangle, Finned Fish, W-Wing, WXYZ-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 (23)
  1. Step 5 · 2-String Kite advanced
    Rules out 5 from R7C9.
  2. Step 6 · Empty Rectangle advanced
    Rules out 5 from R1C9.
  3. Step 7 · WXYZ-Wing expert
    Rules out 2 from R7C2.
  4. Step 8 · ALS-XZ expert
    Rules out 4 from R6C2, R6C3.
  5. Step 12 · ALS-XZ expert
    Rules out 5 from R2C8, R2C9.
  6. Step 13 · ALS-XZ expert
    Rules out 4 from R5C9.
  7. Step 15 · ALS-XZ expert
    Rules out 1 from R7C9, R9C9.
  8. Step 16 · ALS-XZ expert
    Rules out 5 from R9C9.
  9. Step 17 · ALS-XZ expert
    Rules out 9 from R7C9, R9C9.
  10. Step 18 · Nice Loops/AICs expert
    Rules out 8 from R1C9.
  11. Step 19 · Nice Loops/AICs expert
    Rules out 8 from R9C7.
  12. Step 21 · Nice Loops/AICs expert
    Rules out 1 from R6C9.
  13. Step 26 · Nice Loops/AICs expert
    Rules out 1 from R6C8.
  14. Step 27 · Nice Loops/AICs expert
    Rules out 1 from R9C4.
  15. Step 28 · Cell Forcing Chains expert
    Rules out 3 from R1C4, R4C4, R4C5, R6C1 and 1 more; 4 from R4C6; 5 from R7C2, R9C2.
  16. Step 29 · W-Wing advanced
    Rules out 1 from R4C8.
  17. Step 31 · Coloring/Multi-coloring expert
    Rules out 5 from R1C7, R9C1.
  18. Step 34 · XYZ-Wing advanced
    Rules out 1 from R7C5, R9C5.
  19. Step 35 · XY-Chain expert
    Rules out 9 from R1C6.
  20. Step 36 · XY-Chain expert
    Rules out 9 from R6C4.
  21. Step 39 · XY-Chain expert
    Rules out 1 from R7C8.
  22. Step 40 · Finned Fish expert
    Rules out 1 from R5C4.
  23. Step 46 · XY-Chain expert
    Rules out 5 from R1C8, R4C1.

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.