EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 51: 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 51 of 150 in Extreme Sudoku 1
Difficulty
Expert 7 (expert and beyond), from the middle third of the book
Key technique
Nice Loops/AICs
Hard steps
26 of 51 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 (×3), Finned Fish (×2), XY-Chain (×2), 2-String Kite, Coloring/Multi-coloring, Skyscraper, Sue de Coq, Unique Rectangles, W-Wing, WXYZ-Wing, X-Wing/Swordfish, 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 26)
  1. Step 6 · Skyscraper advanced
    Rules out 8 from R4C4.
  2. Step 7 · Finned Fish expert
    Rules out 8 from R8C2.
  3. Step 8 · WXYZ-Wing expert
    Rules out 8 from R6C1.
  4. Step 9 · Sue de Coq expert
    Rules out 3 from R2C7, R3C9; 4 from R8C8.
  5. Step 10 · ALS-XZ expert
    Rules out 1 from R6C9.
  6. Step 12 · Nice Loops/AICs expert
    Rules out 8 from R6C5.
  7. Step 13 · Nice Loops/AICs expert
    Rules out 3 from R1C4.
  8. Step 14 · Nice Loops/AICs expert
    Rules out 5 from R3C4.
  9. Step 15 · Nice Loops/AICs expert
    Rules out 7 from R8C3.
  10. Step 17 · Nice Loops/AICs expert
    Rules out 9 from R8C3.
  11. Step 19 · 2-String Kite advanced
    Rules out 3 from R1C8.
  12. Step 20 · Finned Fish expert
    Rules out 3 from R4C8.
  13. Step 21 · Coloring/Multi-coloring expert
    Rules out 3 from R9C4.
  14. Step 22 · ALS-XZ expert
    Rules out 8 from R9C4.
  15. Step 23 · Nice Loops/AICs expert
    Rules out 9 from R8C7.
  16. Step 24 · XYZ-Wing advanced
    Rules out 4 from R9C9.
  17. Step 25 · Nice Loops/AICs expert
    Rules out 8 from R9C1.
  18. Step 26 · ALS-XZ expert
    Rules out 3 from R3C1.
  19. Step 31 · XY-Chain expert
    Rules out 8 from R7C4.
  20. Step 32 · Nice Loops/AICs expert
    Rules out 3 from R6C2.
  21. Step 33 · Nice Loops/AICs expert
    Rules out 7 from R4C1.
  22. Step 36 · Unique Rectangles advanced
    Rules out 3 from R4C2; 8 from R4C2.
  23. Step 38 · XY-Chain expert
    Rules out 7 from R6C5, R7C4.
  24. Step 41 · X-Wing/Swordfish advanced
    Rules out 8 from R4C9, R5C4.

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.