EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 145: 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 145 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
23 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: 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 (×3), XY-Chain (×3), Cell Forcing Chains, Empty Rectangle, Finned Fish, Skyscraper, W-Wing, WXYZ-Wing, X-Wing/Swordfish.

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 · Skyscraper advanced
    Rules out 2 from R7C8, R8C4.
  2. Step 6 · ALS-XZ expert
    Rules out 3 from R6C2.
  3. Step 9 · Finned Fish expert
    Rules out 3 from R3C3.
  4. Step 10 · ALS-XZ expert
    Rules out 7 from R1C9, R3C9, R9C9.
  5. Step 11 · ALS-XZ expert
    Rules out 2 from R3C9.
  6. Step 12 · ALS-XZ expert
    Rules out 3 from R4C8.
  7. Step 13 · ALS-XZ expert
    Rules out 3 from R4C2, R4C3.
  8. Step 14 · ALS-XZ expert
    Rules out 3 from R1C1, R2C1, R3C1.
  9. Step 16 · Nice Loops/AICs expert
    Rules out 2 from R3C5.
  10. Step 18 · WXYZ-Wing expert
    Rules out 8 from R3C4.
  11. Step 19 · ALS-XZ expert
    Rules out 5 from R2C4.
  12. Step 20 · ALS-XZ expert
    Rules out 6 from R2C4.
  13. Step 21 · Nice Loops/AICs expert
    Rules out 7 from R9C7.
  14. Step 22 · Cell Forcing Chains expert
    Rules out 6 from R2C2.
  15. Step 25 · Nice Loops/AICs expert
    Rules out 2 from R2C8.
  16. Step 28 · ALS-XZ expert
    Rules out 1 from R4C8.
  17. Step 30 · ALS-XZ expert
    Rules out 2 from R5C9.
  18. Step 34 · W-Wing advanced
    Rules out 7 from R9C3.
  19. Step 35 · Empty Rectangle advanced
    Rules out 7 from R8C7.
  20. Step 37 · XY-Chain expert
    Rules out 7 from R5C3.
  21. Step 40 · XY-Chain expert
    Rules out 7 from R4C9.
  22. Step 41 · X-Wing/Swordfish advanced
    Rules out 7 from R8C6.
  23. Step 42 · XY-Chain expert
    Rules out 8 from R7C4, R7C6.

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.