EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 112: 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 112 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
29 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: ALS-XZ (×5), 2-String Kite (×2), XY-Chain (×2), Cell Forcing Chains, Empty Rectangle, Finned Fish, XY-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 29)
  1. Step 4 · 2-String Kite advanced
    Rules out 5 from R8C1.
  2. Step 5 · Empty Rectangle advanced
    Rules out 6 from R1C4.
  3. Step 6 · Finned Fish expert
    Rules out 5 from R9C1.
  4. Step 7 · Nice Loops/AICs expert
    Rules out 1 from R4C1, R9C3.
  5. Step 9 · 2-String Kite advanced
    Rules out 9 from R6C5.
  6. Step 10 · Nice Loops/AICs expert
    Rules out 2 from R8C1.
  7. Step 12 · ALS-XZ expert
    Rules out 8 from R7C1.
  8. Step 13 · Nice Loops/AICs expert
    Rules out 2 from R1C7.
  9. Step 15 · Nice Loops/AICs expert
    Rules out 8 from R8C1.
  10. Step 16 · ALS-XZ expert
    Rules out 1 from R8C8, R9C1.
  11. Step 19 · ALS-XZ expert
    Rules out 3 from R1C5.
  12. Step 20 · Nice Loops/AICs expert
    Rules out 6 from R8C9.
  13. Step 22 · Nice Loops/AICs expert
    Rules out 4 from R5C8.
  14. Step 24 · Nice Loops/AICs expert
    Rules out 8 from R7C5.
  15. Step 25 · ALS-XZ expert
    Rules out 1 from R2C7.
  16. Step 27 · ALS-XZ expert
    Rules out 9 from R5C1.
  17. Step 28 · Nice Loops/AICs expert
    Rules out 3 from R3C4.
  18. Step 29 · Nice Loops/AICs expert
    Rules out 8 from R4C8.
  19. Step 30 · Nice Loops/AICs expert
    Rules out 9 from R6C1.
  20. Step 31 · Nice Loops/AICs expert
    Rules out 9 from R5C8.
  21. Step 32 · Nice Loops/AICs expert
    Rules out 5 from R6C1.
  22. Step 33 · Nice Loops/AICs expert
    Rules out 5 from R7C8.
  23. Step 37 · Nice Loops/AICs expert
    Rules out 6 from R1C5.
  24. Step 39 · Nice Loops/AICs expert
    Rules out 3 from R3C5.

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.