EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 25: 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 25 of 150 in Extreme Sudoku 1
Difficulty
Expert 5 (expert and beyond), from the opening third of the book
Key technique
ALS-XZ
Hard steps
23 of 43 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: XY-Chain (×7), Nice Loops/AICs (×3), 2-String Kite, 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 (23)
  1. Step 6 · WXYZ-Wing expert
    Rules out 5 from R2C1.
  2. Step 7 · ALS-XZ expert
    Rules out 3 from R2C3, R7C2, R8C2.
  3. Step 8 · ALS-XZ expert
    Rules out 6 from R2C3.
  4. Step 10 · Nice Loops/AICs expert
    Rules out 2 from R8C3.
  5. Step 13 · ALS-XZ expert
    Rules out 8 from R6C7.
  6. Step 14 · ALS-XZ expert
    Rules out 8 from R1C6, R2C9.
  7. Step 16 · XY-Chain expert
    Rules out 6 from R1C9.
  8. Step 17 · XY-Chain expert
    Rules out 6 from R1C7, R3C5.
  9. Step 20 · XY-Chain expert
    Rules out 3 from R1C5.
  10. Step 22 · XY-Chain expert
    Rules out 3 from R8C3.
  11. Step 23 · ALS-XZ expert
    Rules out 3 from R1C9.
  12. Step 24 · ALS-XZ expert
    Rules out 9 from R9C9.
  13. Step 25 · Nice Loops/AICs expert
    Rules out 5 from R7C2.
  14. Step 26 · ALS-XZ expert
    Rules out 6 from R7C3, R9C3.
  15. Step 29 · 2-String Kite advanced
    Rules out 9 from R5C4.
  16. Step 30 · Finned Fish expert
    Rules out 5 from R5C4.
  17. Step 31 · ALS-XZ expert
    Rules out 3 from R7C9.
  18. Step 32 · XY-Chain expert
    Rules out 3 from R3C9.
  19. Step 33 · ALS-XZ expert
    Rules out 9 from R7C3.
  20. Step 34 · ALS-XZ expert
    Rules out 3 from R9C4.
  21. Step 35 · Nice Loops/AICs expert
    Rules out 2 from R1C9, R3C4.
  22. Step 37 · XY-Chain expert
    Rules out 5 from R5C1.
  23. Step 39 · XY-Chain expert
    Rules out 5 from R1C2.

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.