EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 31: 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 31 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
22 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: Nice Loops/AICs (×6), XY-Chain (×6), 2-String Kite, Cell Forcing Chains, Finned Fish.

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 (22)
  1. Step 4 · ALS-XZ expert
    Rules out 8 from R4C7.
  2. Step 5 · ALS-XZ expert
    Rules out 4 from R3C6.
  3. Step 6 · Nice Loops/AICs expert
    Rules out 3 from R2C5.
  4. Step 7 · Nice Loops/AICs expert
    Rules out 6 from R2C2.
  5. Step 8 · ALS-XZ expert
    Rules out 3 from R1C5, R7C4.
  6. Step 12 · XY-Chain expert
    Rules out 2 from R5C3.
  7. Step 13 · ALS-XZ expert
    Rules out 5 from R2C6.
  8. Step 14 · ALS-XZ expert
    Rules out 9 from R7C4.
  9. Step 19 · ALS-XZ expert
    Rules out 1 from R4C2, R9C1.
  10. Step 21 · ALS-XZ expert
    Rules out 6 from R4C1.
  11. Step 22 · Nice Loops/AICs expert
    Rules out 6 from R1C1.
  12. Step 23 · Nice Loops/AICs expert
    Rules out 7 from R1C1.
  13. Step 24 · Nice Loops/AICs expert
    Rules out 3 from R6C4.
  14. Step 25 · Nice Loops/AICs expert
    Rules out 4 from R1C6.
  15. Step 26 · Cell Forcing Chains expert
    Rules out 4 from R1C1.
  16. Step 28 · XY-Chain expert
    Rules out 9 from R1C5.
  17. Step 30 · XY-Chain expert
    Rules out 3 from R4C4.
  18. Step 34 · 2-String Kite advanced
    Rules out 7 from R4C2.
  19. Step 35 · Finned Fish expert
    Rules out 7 from R4C3.
  20. Step 37 · XY-Chain expert
    Rules out 6 from R1C5.
  21. Step 39 · XY-Chain expert
    Rules out 5 from R1C6.
  22. Step 40 · XY-Chain expert
    Rules out 5 from R6C4.

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.