EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 55: 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 55 of 150 in Extreme Sudoku 1
Difficulty
Expert 5 (expert and beyond), from the middle third of the book
Key technique
ALS-XZ
Hard steps
16 of 42 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 (×3), Cell Forcing Chains, Skyscraper, W-Wing, WXYZ-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 (16)
  1. Step 7 · WXYZ-Wing expert
    Rules out 9 from R1C7.
  2. Step 8 · ALS-XZ expert
    Rules out 9 from R5C6.
  3. Step 10 · ALS-XZ expert
    Rules out 7 from R3C2.
  4. Step 11 · ALS-XZ expert
    Rules out 4 from R4C5.
  5. Step 13 · ALS-XZ expert
    Rules out 7 from R7C5.
  6. Step 15 · Nice Loops/AICs expert
    Rules out 7 from R3C3.
  7. Step 17 · Cell Forcing Chains expert
    Rules out 9 from R1C5.
  8. Step 19 · X-Wing/Swordfish advanced
    Rules out 9 from R3C8.
  9. Step 20 · ALS-XZ expert
    Rules out 2 from R4C3.
  10. Step 21 · ALS-XZ expert
    Rules out 9 from R2C5.
  11. Step 24 · Nice Loops/AICs expert
    Rules out 7 from R5C6.
  12. Step 26 · ALS-XZ expert
    Rules out 2 from R6C8.
  13. Step 27 · Nice Loops/AICs expert
    Rules out 9 from R3C5.
  14. Step 30 · W-Wing advanced
    Rules out 5 from R2C2.
  15. Step 34 · XY-Chain expert
    Rules out 8 from R4C6.
  16. Step 38 · Skyscraper advanced
    Rules out 2 from R1C8, R2C2, R2C3.

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.