EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 56: 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 56 of 150 in Extreme Sudoku 1
Difficulty
Expert 6 (expert and beyond), from the middle third of the book
Key technique
Nice Loops/AICs
Hard steps
27 of 57 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), ALS-XZ (×2), Empty Rectangle (×2), W-Wing (×2), Cell Forcing Chains, Skyscraper, Sue de Coq, X-Wing/Swordfish, 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 (24 of 27)
  1. Step 5 · Empty Rectangle advanced
    Rules out 3 from R6C5.
  2. Step 6 · Finned Fish expert
    Rules out 8 from R3C5.
  3. Step 7 · ALS-XZ expert
    Rules out 1 from R9C8.
  4. Step 8 · Nice Loops/AICs expert
    Rules out 5 from R8C4.
  5. Step 9 · Nice Loops/AICs expert
    Rules out 6 from R5C5.
  6. Step 10 · Nice Loops/AICs expert
    Rules out 5 from R9C5.
  7. Step 11 · Nice Loops/AICs expert
    Rules out 5 from R7C5.
  8. Step 12 · Nice Loops/AICs expert
    Rules out 5 from R7C4.
  9. Step 13 · Nice Loops/AICs expert
    Rules out 5 from R5C5.
  10. Step 14 · Nice Loops/AICs expert
    Rules out 3 from R5C5.
  11. Step 16 · Nice Loops/AICs expert
    Rules out 5 from R5C6.
  12. Step 17 · Cell Forcing Chains expert
    Rules out 8 from R1C3.
  13. Step 22 · Finned Fish expert
    Rules out 1 from R8C1.
  14. Step 23 · XY-Chain expert
    Rules out 8 from R5C6.
  15. Step 28 · Nice Loops/AICs expert
    Rules out 1 from R3C5.
  16. Step 29 · W-Wing advanced
    Rules out 5 from R6C6.
  17. Step 30 · Nice Loops/AICs expert
    Rules out 5 from R6C1.
  18. Step 31 · Nice Loops/AICs expert
    Rules out 6 from R6C1.
  19. Step 34 · Nice Loops/AICs expert
    Rules out 5 from R8C8.
  20. Step 35 · Nice Loops/AICs expert
    Rules out 3 from R8C8.
  21. Step 37 · ALS-XZ expert
    Rules out 5 from R6C7.
  22. Step 38 · Empty Rectangle advanced
    Rules out 5 from R7C9.
  23. Step 39 · W-Wing advanced
    Rules out 3 from R6C9, R8C7.
  24. Step 41 · Sue de Coq expert
    Rules out 8 from R1C7; 9 from R7C9, R8C9.

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.