EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 89: 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 89 of 150 in Extreme Sudoku 1
Difficulty
Expert 6 (expert and beyond), from the middle third of the book
Key technique
ALS-XZ
Hard steps
28 of 53 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 (×9), XY-Chain (×4), 2-String Kite, Cell Forcing Chains, Empty Rectangle, Finned Fish, 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 28)
  1. Step 3 · 2-String Kite advanced
    Rules out 4 from R7C8.
  2. Step 4 · Finned Fish expert
    Rules out 8 from R2C7, R2C9.
  3. Step 5 · WXYZ-Wing expert
    Rules out 2 from R2C8.
  4. Step 6 · ALS-XZ expert
    Rules out 4 from R1C7, R1C9.
  5. Step 8 · Nice Loops/AICs expert
    Rules out 9 from R2C2.
  6. Step 12 · ALS-XZ expert
    Rules out 4 from R1C8, R3C6.
  7. Step 14 · Empty Rectangle advanced
    Rules out 2 from R4C3.
  8. Step 15 · ALS-XZ expert
    Rules out 4 from R9C4.
  9. Step 16 · ALS-XZ expert
    Rules out 1 from R2C4.
  10. Step 18 · XY-Chain expert
    Rules out 5 from R7C4.
  11. Step 19 · ALS-XZ expert
    Rules out 5 from R8C4.
  12. Step 20 · ALS-XZ expert
    Rules out 2 from R5C7.
  13. Step 21 · ALS-XZ expert
    Rules out 6 from R9C7.
  14. Step 22 · Nice Loops/AICs expert
    Rules out 8 from R1C9.
  15. Step 23 · Nice Loops/AICs expert
    Rules out 7 from R6C9.
  16. Step 25 · Nice Loops/AICs expert
    Rules out 8 from R6C7.
  17. Step 26 · Nice Loops/AICs expert
    Rules out 4 from R8C4.
  18. Step 27 · XY-Chain expert
    Rules out 7 from R7C4, R8C1.
  19. Step 29 · Nice Loops/AICs expert
    Rules out 9 from R6C2.
  20. Step 30 · ALS-XZ expert
    Rules out 9 from R8C1.
  21. Step 32 · ALS-XZ expert
    Rules out 1 from R1C1.
  22. Step 33 · Nice Loops/AICs expert
    Rules out 9 from R5C7.
  23. Step 34 · Nice Loops/AICs expert
    Rules out 9 from R6C7.
  24. Step 35 · Nice Loops/AICs expert
    Rules out 4 from R8C3, R9C6.

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.