EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 137: 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 137 of 150 in Extreme Sudoku 1
Difficulty
Expert 6 (expert and beyond), from the final, hardest third of the book
Key technique
ALS-XZ
Hard steps
27 of 55 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 (×6), XY-Chain (×4), Empty Rectangle (×2), XY-Wing (×2), Cell Forcing Chains, Finned Fish, Skyscraper, W-Wing, 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 (24 of 27)
  1. Step 3 · Skyscraper advanced
    Rules out 9 from R3C3.
  2. Step 6 · XY-Wing advanced
    Rules out 2 from R8C5.
  3. Step 8 · ALS-XZ expert
    Rules out 6 from R5C2, R6C2.
  4. Step 10 · ALS-XZ expert
    Rules out 3 from R8C9, R9C9.
  5. Step 11 · ALS-XZ expert
    Rules out 2 from R8C9, R9C9.
  6. Step 12 · ALS-XZ expert
    Rules out 4 from R5C7, R6C7.
  7. Step 13 · ALS-XZ expert
    Rules out 5 from R6C7.
  8. Step 14 · ALS-XZ expert
    Rules out 9 from R7C4.
  9. Step 15 · Nice Loops/AICs expert
    Rules out 9 from R7C7.
  10. Step 16 · Cell Forcing Chains expert
    Rules out 5 from R1C6.
  11. Step 21 · XY-Chain expert
    Rules out 2 from R5C9.
  12. Step 22 · WXYZ-Wing expert
    Rules out 1 from R5C7.
  13. Step 23 · Nice Loops/AICs expert
    Rules out 3 from R7C4.
  14. Step 24 · Nice Loops/AICs expert
    Rules out 3 from R9C8.
  15. Step 25 · Empty Rectangle advanced
    Rules out 3 from R8C4.
  16. Step 27 · ALS-XZ expert
    Rules out 2 from R9C3.
  17. Step 29 · Nice Loops/AICs expert
    Rules out 4 from R1C3.
  18. Step 30 · Nice Loops/AICs expert
    Rules out 6 from R6C5.
  19. Step 31 · ALS-XZ expert
    Rules out 4 from R6C4.
  20. Step 32 · Nice Loops/AICs expert
    Rules out 4 from R8C9.
  21. Step 39 · Empty Rectangle advanced
    Rules out 9 from R8C2.
  22. Step 40 · W-Wing advanced
    Rules out 9 from R9C2, R9C3.
  23. Step 42 · Finned Fish expert
    Rules out 4 from R8C8.
  24. Step 44 · XY-Chain expert
    Rules out 2 from R7C3.

The book

Classic 9×9 sudoku with the warm-up taken out. Every grid sits at the top of the expert range or beyond it, and the book ramps from hard to brutal.

150 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.

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More step-by-step solutions: Extreme Killer Sudoku 1 · Extreme Sudoku 2 · Extreme Killer Sudoku 2 · Extreme Sudoku 3 · Extreme Killer Sudoku 3.