EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 143: 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 143 of 150 in Extreme Sudoku 1
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), Skyscraper (×2), Cell Forcing Chains, 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 (23)
  1. Step 5 · Finned Fish expert
    Rules out 9 from R9C5.
  2. Step 6 · Sue de Coq expert
    Rules out 8 from R2C7, R7C7, R8C7; 9 from R3C7, R7C7, R8C7; 3 from R4C8.
  3. Step 8 · ALS-XZ expert
    Rules out 7 from R2C7.
  4. Step 9 · ALS-XZ expert
    Rules out 1 from R4C1, R6C1.
  5. Step 10 · Cell Forcing Chains expert
    Rules out 1 from R1C9.
  6. Step 13 · Skyscraper advanced
    Rules out 1 from R3C2.
  7. Step 15 · ALS-XZ expert
    Rules out 7 from R8C2.
  8. Step 16 · ALS-XZ expert
    Rules out 7 from R3C1, R6C1.
  9. Step 17 · WXYZ-Wing expert
    Rules out 3 from R6C6.
  10. Step 18 · ALS-XZ expert
    Rules out 1 from R3C1.
  11. Step 19 · Nice Loops/AICs expert
    Rules out 1 from R1C6.
  12. Step 23 · Nice Loops/AICs expert
    Rules out 5 from R6C6.
  13. Step 24 · Nice Loops/AICs expert
    Rules out 5 from R4C4.
  14. Step 25 · ALS-XZ expert
    Rules out 6 from R4C6.
  15. Step 26 · ALS-XZ expert
    Rules out 3 from R4C4, R4C5.
  16. Step 27 · Nice Loops/AICs expert
    Rules out 1 from R4C6.
  17. Step 29 · XY-Chain expert
    Rules out 8 from R9C2.
  18. Step 30 · ALS-XZ expert
    Rules out 2 from R7C4.
  19. Step 31 · Nice Loops/AICs expert
    Rules out 5 from R4C1, R6C5.
  20. Step 33 · XY-Chain expert
    Rules out 8 from R7C1.
  21. Step 40 · Skyscraper advanced
    Rules out 3 from R1C6, R3C7.
  22. Step 41 · XY-Chain expert
    Rules out 3 from R5C8.
  23. Step 45 · XY-Chain expert
    Rules out 6 from R1C7, R3C4, R3C5.

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.