EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 113: 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 113 of 150 in Extreme Sudoku 3
Difficulty
Expert 7 (expert and beyond), from the final, hardest third of the book
Key technique
Nice Loops/AICs
Hard steps
21 of 42 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), XY-Chain (×3), Skyscraper (×2), Cell Forcing Chains, Empty Rectangle, Finned Fish, Sue de Coq, WXYZ-Wing, 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 (21)
  1. Step 6 · Sue de Coq expert
    Rules out 6 from R4C5, R4C6, R6C5, R6C6; 5 from R4C6; 7 from R5C9.
  2. Step 9 · ALS-XZ expert
    Rules out 8 from R7C6.
  3. Step 11 · Nice Loops/AICs expert
    Rules out 6 from R3C8.
  4. Step 13 · Nice Loops/AICs expert
    Rules out 2 from R7C9.
  5. Step 14 · XY-Wing advanced
    Rules out 8 from R2C9.
  6. Step 15 · Nice Loops/AICs expert
    Rules out 4 from R3C3.
  7. Step 16 · Nice Loops/AICs expert
    Rules out 9 from R8C9.
  8. Step 17 · Nice Loops/AICs expert
    Rules out 7 from R2C9.
  9. Step 18 · Cell Forcing Chains expert
    Rules out 4 from R2C2.
  10. Step 20 · Empty Rectangle advanced
    Rules out 4 from R7C6.
  11. Step 23 · Skyscraper advanced
    Rules out 3 from R3C5, R9C4.
  12. Step 24 · Skyscraper advanced
    Rules out 4 from R3C8.
  13. Step 25 · Finned Fish expert
    Rules out 4 from R1C6.
  14. Step 26 · ALS-XZ expert
    Rules out 9 from R8C5, R9C5.
  15. Step 27 · Nice Loops/AICs expert
    Rules out 9 from R2C9.
  16. Step 29 · Nice Loops/AICs expert
    Rules out 6 from R8C5.
  17. Step 32 · XY-Chain expert
    Rules out 8 from R3C9.
  18. Step 35 · XY-Chain expert
    Rules out 6 from R5C4.
  19. Step 36 · XY-Chain expert
    Rules out 9 from R3C4.
  20. Step 37 · WXYZ-Wing expert
    Rules out 9 from R3C6.
  21. Step 38 · ALS-XZ expert
    Rules out 4 from R2C7.

The book

Volume three: 150 new classic 9×9 grids, none repeated from books 1 or 2, ramping from hard to brutal.

150 new 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.

On Amazon from 8 Dec About the book

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More step-by-step solutions: Extreme Sudoku 1 · Extreme Killer Sudoku 1 · Extreme Sudoku 2 · Extreme Killer Sudoku 2 · Extreme Killer Sudoku 3.