EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 105: 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 105 of 150 in Extreme Sudoku 1
Difficulty
Expert 5 (expert and beyond), from the final, hardest third of the book
Key technique
Nice Loops/AICs
Hard steps
25 of 49 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 (×3), 2-String Kite (×2), Empty Rectangle (×2), X-Wing/Swordfish (×2), Cell Forcing Chains, Skyscraper, WXYZ-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 4 · Skyscraper advanced
    Rules out 5 from R1C3, R7C1, R8C1.
  2. Step 6 · Empty Rectangle advanced
    Rules out 6 from R8C2.
  3. Step 7 · Finned Fish expert
    Rules out 8 from R3C7.
  4. Step 8 · WXYZ-Wing expert
    Rules out 7 from R1C9.
  5. Step 9 · ALS-XZ expert
    Rules out 6 from R3C9.
  6. Step 12 · X-Wing/Swordfish advanced
    Rules out 8 from R3C2, R3C3, R4C7, R7C3 and 4 more.
  7. Step 13 · Empty Rectangle advanced
    Rules out 6 from R8C4.
  8. Step 14 · Finned Fish expert
    Rules out 7 from R3C4.
  9. Step 17 · 2-String Kite advanced
    Rules out 3 from R5C2.
  10. Step 18 · Nice Loops/AICs expert
    Rules out 1 from R8C7.
  11. Step 19 · Nice Loops/AICs expert
    Rules out 7 from R4C6, R6C7.
  12. Step 21 · ALS-XZ expert
    Rules out 7 from R3C2.
  13. Step 22 · Nice Loops/AICs expert
    Rules out 4 from R9C5.
  14. Step 23 · X-Wing/Swordfish advanced
    Rules out 4 from R3C4, R4C2, R8C2.
  15. Step 24 · ALS-XZ expert
    Rules out 6 from R3C2.
  16. Step 25 · Nice Loops/AICs expert
    Rules out 1 from R3C7.
  17. Step 27 · Nice Loops/AICs expert
    Rules out 4 from R4C8.
  18. Step 29 · 2-String Kite advanced
    Rules out 2 from R8C7.
  19. Step 30 · Nice Loops/AICs expert
    Rules out 6 from R3C3.
  20. Step 31 · Finned Fish expert
    Rules out 6 from R8C1.
  21. Step 32 · Nice Loops/AICs expert
    Rules out 8 from R9C3.
  22. Step 33 · Nice Loops/AICs expert
    Rules out 2 from R8C1.
  23. Step 34 · Cell Forcing Chains expert
    Rules out 6 from R1C5.
  24. Step 37 · XYZ-Wing advanced
    Rules out 6 from R2C2.

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.