EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 53: 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 53 of 150 in Extreme Sudoku 1
Difficulty
Expert 7 (expert and beyond), from the middle third of the book
Key technique
ALS-XZ
Hard steps
15 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), Finned Fish (×2), XY-Chain (×2), Cell Forcing Chains, Coloring/Multi-coloring, Empty Rectangle, W-Wing, 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 (15)
  1. Step 10 · Finned Fish expert
    Rules out 3 from R6C9.
  2. Step 11 · ALS-XZ expert
    Rules out 6 from R1C1.
  3. Step 12 · ALS-XZ expert
    Rules out 3 from R1C8.
  4. Step 13 · Nice Loops/AICs expert
    Rules out 3 from R2C8.
  5. Step 16 · ALS-XZ expert
    Rules out 5 from R1C1.
  6. Step 18 · Finned Fish expert
    Rules out 2 from R2C6.
  7. Step 19 · Coloring/Multi-coloring expert
    Rules out 2 from R9C1.
  8. Step 21 · Nice Loops/AICs expert
    Rules out 6 from R2C6.
  9. Step 22 · WXYZ-Wing expert
    Rules out 5 from R2C1, R3C6.
  10. Step 24 · Nice Loops/AICs expert
    Rules out 8 from R5C6.
  11. Step 26 · Cell Forcing Chains expert
    Rules out 2 from R1C1.
  12. Step 29 · Empty Rectangle advanced
    Rules out 2 from R7C5.
  13. Step 31 · W-Wing advanced
    Rules out 6 from R1C5, R3C1, R3C3.
  14. Step 36 · XY-Chain expert
    Rules out 6 from R6C2.
  15. Step 39 · XY-Chain expert
    Rules out 6 from R2C1, R2C2.

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.