EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, 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 2
Difficulty
Expert 6 (expert and beyond), from the opening third of the book
Key technique
Nice Loops/AICs
Hard steps
21 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: Nice Loops/AICs

An alternating chain of strong and weak links. Whichever end is true, the conclusion holds, so the digit at the marked cell is ruled out.

Other advanced and expert techniques in this solve: XY-Wing (×3), ALS-XZ (×2), Finned Fish (×2), XYZ-Wing (×2), 2-String Kite, Cell Forcing Chains, Sue de Coq, W-Wing, WXYZ-Wing, X-Wing/Swordfish.

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 (21)
  1. Step 5 · Finned Fish expert
    Rules out 1 from R8C6.
  2. Step 6 · ALS-XZ expert
    Rules out 2 from R9C6.
  3. Step 8 · XY-Wing advanced
    Rules out 9 from R1C8, R8C9.
  4. Step 10 · ALS-XZ expert
    Rules out 7 from R6C1.
  5. Step 11 · Nice Loops/AICs expert
    Rules out 2 from R1C8.
  6. Step 14 · Nice Loops/AICs expert
    Rules out 2 from R6C7.
  7. Step 15 · Nice Loops/AICs expert
    Rules out 1 from R8C4.
  8. Step 16 · Nice Loops/AICs expert
    Rules out 1 from R7C5.
  9. Step 17 · Nice Loops/AICs expert
    Rules out 1 from R6C7.
  10. Step 18 · Nice Loops/AICs expert
    Rules out 8 from R6C1.
  11. Step 19 · Cell Forcing Chains expert
    Rules out 8 from R1C5.
  12. Step 23 · XYZ-Wing advanced
    Rules out 7 from R3C1.
  13. Step 24 · Finned Fish expert
    Rules out 5 from R4C3, R5C3.
  14. Step 28 · W-Wing advanced
    Rules out 1 from R2C9.
  15. Step 29 · Sue de Coq expert
    Rules out 1 from R5C7.
  16. Step 30 · 2-String Kite advanced
    Rules out 1 from R3C5.
  17. Step 31 · WXYZ-Wing expert
    Rules out 5 from R2C6.
  18. Step 32 · XY-Wing advanced
    Rules out 4 from R2C1.
  19. Step 34 · X-Wing/Swordfish advanced
    Rules out 1 from R3C7, R4C5, R4C9.
  20. Step 35 · XYZ-Wing advanced
    Rules out 5 from R4C5.
  21. Step 37 · XY-Wing advanced
    Rules out 1 from R6C1, R6C2.

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.