EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 125: 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 125 of 150 in Extreme Sudoku 2
Difficulty
Expert 7 (expert and beyond), from the final, hardest third of the book
Key technique
ALS-XZ
Hard steps
26 of 51 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, Cell Forcing Chains, Finned Fish, Sue de Coq, WXYZ-Wing, X-Wing/Swordfish, XY-Wing, XYZ-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 26)
  1. Step 3 · 2-String Kite advanced
    Rules out 6 from R5C9.
  2. Step 4 · XYZ-Wing advanced
    Rules out 1 from R6C4.
  3. Step 5 · XY-Chain expert
    Rules out 8 from R3C2.
  4. Step 6 · XY-Chain expert
    Rules out 3 from R6C6, R7C6.
  5. Step 8 · XY-Chain expert
    Rules out 1 from R5C7, R5C9.
  6. Step 11 · ALS-XZ expert
    Rules out 8 from R7C2, R8C2.
  7. Step 13 · ALS-XZ expert
    Rules out 5 from R8C9.
  8. Step 14 · ALS-XZ expert
    Rules out 3 from R1C4, R3C4.
  9. Step 15 · WXYZ-Wing expert
    Rules out 7 from R3C3.
  10. Step 21 · Cell Forcing Chains expert
    Rules out 7 from R1C1.
  11. Step 23 · Nice Loops/AICs expert
    Rules out 3 from R4C5.
  12. Step 25 · XY-Chain expert
    Rules out 8 from R8C5.
  13. Step 26 · XY-Chain expert
    Rules out 5 from R9C9.
  14. Step 28 · XY-Chain expert
    Rules out 8 from R7C1.
  15. Step 30 · Sue de Coq expert
    Rules out 5 from R7C4, R8C4; 8 from R7C5; 3 from R9C7, R9C8.
  16. Step 31 · Finned Fish expert
    Rules out 6 from R7C4.
  17. Step 32 · ALS-XZ expert
    Rules out 7 from R2C7.
  18. Step 33 · ALS-XZ expert
    Rules out 3 from R7C8.
  19. Step 34 · ALS-XZ expert
    Rules out 3 from R8C7.
  20. Step 35 · ALS-XZ expert
    Rules out 6 from R2C9.
  21. Step 36 · ALS-XZ expert
    Rules out 3 from R7C7.
  22. Step 37 · Nice Loops/AICs expert
    Rules out 2 from R8C5.
  23. Step 38 · Nice Loops/AICs expert
    Rules out 3 from R8C8.
  24. Step 44 · XY-Wing advanced
    Rules out 6 from R7C5, R9C9.

The book

Volume two: 150 new classic 9×9 grids, none repeated from book 1, ramping from hard to brutal.

150 new 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 Sudoku 1 · Extreme Killer Sudoku 1 · Extreme Killer Sudoku 2 · Extreme Sudoku 3 · Extreme Killer Sudoku 3.