EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 76: 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 76 of 150 in Extreme Sudoku 2
Difficulty
Expert 7 (expert and beyond), from the middle third of the book
Key technique
Nice Loops/AICs
Hard steps
21 of 41 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: ALS-XZ (×5), Finned Fish (×2), XY-Wing (×2), 2-String Kite, Cell Forcing Chains, Empty Rectangle, Sue de Coq, WXYZ-Wing, 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 (21)
  1. Step 3 · Finned Fish expert
    Rules out 1 from R9C5.
  2. Step 4 · Sue de Coq expert
    Rules out 3 from R1C2, R3C2; 7 from R1C2, R3C2; 1 from R9C1.
  3. Step 5 · ALS-XZ expert
    Rules out 5 from R1C9.
  4. Step 6 · ALS-XZ expert
    Rules out 3 from R2C1.
  5. Step 7 · ALS-XZ expert
    Rules out 7 from R2C1.
  6. Step 9 · Nice Loops/AICs expert
    Rules out 9 from R2C9.
  7. Step 11 · Nice Loops/AICs expert
    Rules out 8 from R6C5.
  8. Step 12 · ALS-XZ expert
    Rules out 1 from R5C4, R8C5.
  9. Step 13 · Nice Loops/AICs expert
    Rules out 8 from R4C5.
  10. Step 15 · ALS-XZ expert
    Rules out 4 from R3C5, R4C6.
  11. Step 19 · Finned Fish expert
    Rules out 9 from R4C8.
  12. Step 20 · Nice Loops/AICs expert
    Rules out 3 from R6C9.
  13. Step 21 · Nice Loops/AICs expert
    Rules out 3 from R4C8.
  14. Step 22 · Nice Loops/AICs expert
    Rules out 5 from R4C8.
  15. Step 23 · WXYZ-Wing expert
    Rules out 7 from R6C9.
  16. Step 24 · Cell Forcing Chains expert
    Rules out 3 from R1C4; 7 from R2C5, R5C4; 9 from R4C7, R5C4.
  17. Step 25 · 2-String Kite advanced
    Rules out 7 from R5C9.
  18. Step 29 · Empty Rectangle advanced
    Rules out 3 from R7C2.
  19. Step 30 · XY-Wing advanced
    Rules out 7 from R2C4.
  20. Step 34 · XY-Wing advanced
    Rules out 3 from R6C2.
  21. Step 36 · XY-Chain expert
    Rules out 3 from R9C1.

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.