EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 132: 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 132 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
17 of 39 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: Empty Rectangle (×3), WXYZ-Wing (×2), Cell Forcing Chains, Finned Fish, Nice Loops/AICs, Sue de Coq, Unique Rectangles, W-Wing, X-Wing/Swordfish, XY-Chain.

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 (17)
  1. Step 5 · Empty Rectangle advanced
    Rules out 8 from R1C7.
  2. Step 8 · WXYZ-Wing expert
    Rules out 8 from R7C7.
  3. Step 9 · Sue de Coq expert
    Rules out 2 from R8C1.
  4. Step 11 · ALS-XZ expert
    Rules out 6 from R7C2.
  5. Step 13 · Unique Rectangles advanced
    Rules out 2 from R9C7; 4 from R9C7.
  6. Step 16 · ALS-XZ expert
    Rules out 6 from R1C3.
  7. Step 17 · Nice Loops/AICs expert
    Rules out 6 from R1C4.
  8. Step 18 · Cell Forcing Chains expert
    Rules out 1 from R1C4; 5 from R1C4; 7 from R1C4.
  9. Step 20 · Empty Rectangle advanced
    Rules out 4 from R4C3.
  10. Step 22 · WXYZ-Wing expert
    Rules out 6 from R1C2.
  11. Step 23 · Empty Rectangle advanced
    Rules out 6 from R3C4.
  12. Step 24 · ALS-XZ expert
    Rules out 4 from R1C3.
  13. Step 26 · ALS-XZ expert
    Rules out 6 from R5C5.
  14. Step 27 · Finned Fish expert
    Rules out 6 from R4C3.
  15. Step 32 · X-Wing/Swordfish advanced
    Rules out 6 from R3C3.
  16. Step 33 · XY-Chain expert
    Rules out 7 from R1C5.
  17. Step 35 · W-Wing advanced
    Rules out 5 from R1C1, 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.