EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 129: 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 129 of 150 in Extreme Sudoku 2
Difficulty
Expert 5 (expert and beyond), from the final, hardest third of the book
Key technique
Nice Loops/AICs
Hard steps
19 of 44 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, Cell Forcing Chains, Finned Fish, W-Wing, X-Wing/Swordfish, XY-Wing, XYZ-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 5 · 2-String Kite advanced
    Rules out 8 from R8C2.
  2. Step 6 · XYZ-Wing advanced
    Rules out 3 from R3C2.
  3. Step 7 · ALS-XZ expert
    Rules out 3 from R7C1.
  4. Step 8 · ALS-XZ expert
    Rules out 7 from R3C2.
  5. Step 10 · ALS-XZ expert
    Rules out 7 from R2C2.
  6. Step 12 · Cell Forcing Chains expert
    Rules out 3 from R2C2.
  7. Step 14 · Nice Loops/AICs expert
    Rules out 4 from R7C1.
  8. Step 15 · Nice Loops/AICs expert
    Rules out 3 from R1C1.
  9. Step 18 · Finned Fish expert
    Rules out 7 from R1C6.
  10. Step 19 · Nice Loops/AICs expert
    Rules out 7 from R1C7.
  11. Step 20 · Nice Loops/AICs expert
    Rules out 5 from R4C7.
  12. Step 22 · Nice Loops/AICs expert
    Rules out 7 from R1C5.
  13. Step 24 · X-Wing/Swordfish advanced
    Rules out 7 from R4C6.
  14. Step 25 · XY-Wing advanced
    Rules out 3 from R3C7.
  15. Step 28 · ALS-XZ expert
    Rules out 7 from R5C9.
  16. Step 29 · Nice Loops/AICs expert
    Rules out 8 from R1C4.
  17. Step 30 · XY-Chain expert
    Rules out 1 from R1C6, R6C4.
  18. Step 33 · W-Wing advanced
    Rules out 2 from R4C8, R6C1, R6C2.
  19. Step 40 · XY-Chain expert
    Rules out 7 from R2C3.

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.