EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 3: 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 3 of 150 in Extreme Sudoku 2
Difficulty
Expert 5 (expert and beyond), from the opening third of the book
Key technique
Nice Loops/AICs
Hard steps
20 of 43 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 (×4), XY-Chain (×2), 2-String Kite, Finned Fish, 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 (20)
  1. Step 9 · 2-String Kite advanced
    Rules out 5 from R4C3.
  2. Step 10 · Finned Fish expert
    Rules out 7 from R8C9.
  3. Step 11 · WXYZ-Wing expert
    Rules out 5 from R6C3.
  4. Step 12 · ALS-XZ expert
    Rules out 3 from R8C3.
  5. Step 13 · ALS-XZ expert
    Rules out 7 from R4C1, R6C2.
  6. Step 14 · ALS-XZ expert
    Rules out 6 from R6C2.
  7. Step 15 · Nice Loops/AICs expert
    Rules out 2 from R8C2.
  8. Step 16 · Nice Loops/AICs expert
    Rules out 5 from R8C3.
  9. Step 17 · Nice Loops/AICs expert
    Rules out 5 from R6C2.
  10. Step 18 · Nice Loops/AICs expert
    Rules out 8 from R4C8.
  11. Step 19 · Nice Loops/AICs expert
    Rules out 8 from R4C9.
  12. Step 21 · ALS-XZ expert
    Rules out 2 from R8C9.
  13. Step 22 · Nice Loops/AICs expert
    Rules out 5 from R8C1.
  14. Step 24 · Nice Loops/AICs expert
    Rules out 8 from R8C9.
  15. Step 28 · Nice Loops/AICs expert
    Rules out 6 from R6C3.
  16. Step 29 · XY-Wing advanced
    Rules out 7 from R5C2.
  17. Step 30 · Nice Loops/AICs expert
    Rules out 7 from R4C9.
  18. Step 32 · Nice Loops/AICs expert
    Rules out 5 from R4C1.
  19. Step 36 · XY-Chain expert
    Rules out 8 from R7C2.
  20. Step 40 · XY-Chain expert
    Rules out 4 from R2C3, R4C1.

The book

Volume two: 150 new classic 9×9 grids, none repeated from book 1, 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.

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