EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 43: 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 43 of 150 in Extreme Sudoku 2
Difficulty
Expert 7 (expert and beyond), from the opening third of the book
Key technique
Nice Loops/AICs
Hard steps
25 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: Finned Fish (×3), W-Wing (×3), ALS-XZ (×2), Cell Forcing Chains, Coloring/Multi-coloring, Empty Rectangle, Skyscraper, WXYZ-Wing, XY-Chain, XY-Wing, XYZ-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 (24 of 25)
  1. Step 3 · Skyscraper advanced
    Rules out 1 from R4C4, R7C6, R8C6.
  2. Step 4 · Empty Rectangle advanced
    Rules out 2 from R5C8.
  3. Step 5 · WXYZ-Wing expert
    Rules out 2 from R1C7.
  4. Step 6 · ALS-XZ expert
    Rules out 6 from R4C7.
  5. Step 7 · Nice Loops/AICs expert
    Rules out 6 from R1C2.
  6. Step 8 · Nice Loops/AICs expert
    Rules out 9 from R4C7.
  7. Step 9 · Nice Loops/AICs expert
    Rules out 2 from R8C8.
  8. Step 10 · Nice Loops/AICs expert
    Rules out 7 from R4C8.
  9. Step 12 · Nice Loops/AICs expert
    Rules out 2 from R1C2; 3 from R1C2.
  10. Step 13 · Nice Loops/AICs expert
    Rules out 1 from R5C1.
  11. Step 15 · Nice Loops/AICs expert
    Rules out 3 from R5C1; 2 from R5C7.
  12. Step 16 · Finned Fish expert
    Rules out 3 from R7C5.
  13. Step 17 · Finned Fish expert
    Rules out 3 from R8C5.
  14. Step 18 · Nice Loops/AICs expert
    Rules out 6 from R4C8.
  15. Step 19 · Cell Forcing Chains expert
    Rules out 6 from R1C1, R5C7; 2 from R1C9, R8C6; 3 from R2C2, R5C5, R6C7.
  16. Step 23 · Nice Loops/AICs expert
    Rules out 6 from R4C4, R7C5, R8C5.
  17. Step 24 · XY-Wing advanced
    Rules out 3 from R4C6.
  18. Step 25 · Finned Fish expert
    Rules out 6 from R7C2.
  19. Step 26 · XY-Chain expert
    Rules out 6 from R8C7.
  20. Step 28 · Coloring/Multi-coloring expert
    Rules out 3 from R4C2.
  21. Step 29 · W-Wing advanced
    Rules out 1 from R4C1, R7C2, R8C2.
  22. Step 31 · XYZ-Wing advanced
    Rules out 3 from R8C3.
  23. Step 32 · W-Wing advanced
    Rules out 3 from R7C4.
  24. Step 33 · ALS-XZ expert
    Rules out 2 from R2C2.

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.