EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 111: 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 111 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
19 of 48 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: XY-Chain (×4), Finned Fish (×3), Skyscraper (×2), ALS-XZ, Cell Forcing Chains, W-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 (19)
  1. Step 7 · Skyscraper advanced
    Rules out 7 from R5C3.
  2. Step 10 · Skyscraper advanced
    Rules out 3 from R7C5, R9C1.
  3. Step 11 · Finned Fish expert
    Rules out 5 from R6C9.
  4. Step 14 · Nice Loops/AICs expert
    Rules out 4 from R7C5.
  5. Step 15 · Nice Loops/AICs expert
    Rules out 6 from R2C9, R9C8.
  6. Step 16 · Cell Forcing Chains expert
    Rules out 8 from R1C7.
  7. Step 20 · Finned Fish expert
    Rules out 5 from R6C7.
  8. Step 22 · ALS-XZ expert
    Rules out 7 from R2C5.
  9. Step 23 · Nice Loops/AICs expert
    Rules out 7 from R5C5.
  10. Step 24 · Nice Loops/AICs expert
    Rules out 7 from R7C5, R8C5, R9C5.
  11. Step 26 · Nice Loops/AICs expert
    Rules out 5 from R2C5.
  12. Step 27 · Nice Loops/AICs expert
    Rules out 1 from R2C3.
  13. Step 29 · Finned Fish expert
    Rules out 8 from R1C8.
  14. Step 32 · Nice Loops/AICs expert
    Rules out 7 from R9C4.
  15. Step 35 · XY-Chain expert
    Rules out 8 from R2C1, R3C1.
  16. Step 37 · XY-Chain expert
    Rules out 7 from R5C4.
  17. Step 38 · XY-Chain expert
    Rules out 3 from R5C4.
  18. Step 40 · W-Wing advanced
    Rules out 4 from R5C8, R6C5.
  19. Step 44 · XY-Chain expert
    Rules out 8 from R5C3.

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.