EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 126: 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 126 of 150 in Extreme Sudoku 2
Difficulty
Expert 7 (expert and beyond), from the final, hardest third of the book
Key technique
Nice Loops/AICs
Hard steps
21 of 46 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), ALS-XZ (×3), 2-String Kite, Cell Forcing Chains, Coloring/Multi-coloring, Empty Rectangle, Finned Fish, Skyscraper, W-Wing, WXYZ-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 (21)
  1. Step 9 · 2-String Kite advanced
    Rules out 3 from R6C1.
  2. Step 10 · Nice Loops/AICs expert
    Rules out 6 from R8C6.
  3. Step 11 · XYZ-Wing advanced
    Rules out 2 from R8C7.
  4. Step 12 · Nice Loops/AICs expert
    Rules out 2 from R7C8.
  5. Step 13 · Nice Loops/AICs expert
    Rules out 2 from R4C8.
  6. Step 14 · ALS-XZ expert
    Rules out 2 from R7C7.
  7. Step 15 · Cell Forcing Chains expert
    Rules out 2 from R1C1.
  8. Step 17 · ALS-XZ expert
    Rules out 6 from R7C7, R8C7.
  9. Step 20 · Empty Rectangle advanced
    Rules out 6 from R8C1.
  10. Step 21 · Finned Fish expert
    Rules out 6 from R4C1.
  11. Step 22 · Nice Loops/AICs expert
    Rules out 6 from R3C9.
  12. Step 23 · Nice Loops/AICs expert
    Rules out 6 from R3C8, R4C7.
  13. Step 26 · Coloring/Multi-coloring expert
    Rules out 6 from R6C1.
  14. Step 28 · Skyscraper advanced
    Rules out 2 from R8C9.
  15. Step 31 · XY-Chain expert
    Rules out 7 from R8C1.
  16. Step 33 · XY-Chain expert
    Rules out 7 from R8C3.
  17. Step 35 · WXYZ-Wing expert
    Rules out 1 from R7C5.
  18. Step 36 · ALS-XZ expert
    Rules out 5 from R6C3.
  19. Step 37 · XY-Chain expert
    Rules out 3 from R4C3.
  20. Step 42 · W-Wing advanced
    Rules out 7 from R6C4.
  21. Step 43 · XY-Chain expert
    Rules out 3 from R3C9.

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.