EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 65: 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 65 of 150 in Extreme Sudoku 3
Difficulty
Expert 7 (expert and beyond), from the middle third of the book
Key technique
Nice Loops/AICs
Hard steps
21 of 37 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), Cell Forcing Chains, Empty Rectangle, Finned Fish, Sue de Coq, WXYZ-Wing, XY-Chain.

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 3 · Finned Fish expert
    Rules out 4 from R1C7, R3C7.
  2. Step 4 · WXYZ-Wing expert
    Rules out 4 from R3C5.
  3. Step 6 · ALS-XZ expert
    Rules out 7 from R1C1, R1C2.
  4. Step 9 · ALS-XZ expert
    Rules out 9 from R7C2.
  5. Step 10 · Nice Loops/AICs expert
    Rules out 8 from R6C5.
  6. Step 11 · Nice Loops/AICs expert
    Rules out 6 from R2C1.
  7. Step 12 · Nice Loops/AICs expert
    Rules out 6 from R5C3.
  8. Step 13 · Nice Loops/AICs expert
    Rules out 9 from R5C3.
  9. Step 14 · Nice Loops/AICs expert
    Rules out 8 from R6C1.
  10. Step 15 · Nice Loops/AICs expert
    Rules out 8 from R4C1.
  11. Step 16 · ALS-XZ expert
    Rules out 7 from R9C1.
  12. Step 17 · Nice Loops/AICs expert
    Rules out 7 from R7C2.
  13. Step 18 · Nice Loops/AICs expert
    Rules out 8 from R9C4.
  14. Step 19 · Sue de Coq expert
    Rules out 9 from R8C4.
  15. Step 20 · Nice Loops/AICs expert
    Rules out 7 from R2C3.
  16. Step 21 · Nice Loops/AICs expert
    Rules out 1 from R4C4.
  17. Step 22 · Cell Forcing Chains expert
    Rules out 8 from R1C4.
  18. Step 26 · ALS-XZ expert
    Rules out 7 from R3C2.
  19. Step 27 · ALS-XZ expert
    Rules out 4 from R8C1, R9C7, R9C9.
  20. Step 31 · Empty Rectangle advanced
    Rules out 2 from R4C4.
  21. Step 34 · XY-Chain expert
    Rules out 4 from R3C2, R9C1.

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.