EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 137: 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 137 of 150 in Extreme Sudoku 2
Difficulty
Expert 6 (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 (×5), Empty Rectangle (×3), WXYZ-Wing (×2), Cell Forcing Chains, Finned Fish, W-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 5 · Nice Loops/AICs expert
    Rules out 5 from R7C3.
  2. Step 6 · Nice Loops/AICs expert
    Rules out 7 from R9C4.
  3. Step 7 · Nice Loops/AICs expert
    Rules out 9 from R9C4.
  4. Step 8 · Cell Forcing Chains expert
    Rules out 4 from R1C3.
  5. Step 12 · WXYZ-Wing expert
    Rules out 4 from R6C2.
  6. Step 13 · ALS-XZ expert
    Rules out 8 from R1C7.
  7. Step 14 · ALS-XZ expert
    Rules out 2 from R1C5.
  8. Step 16 · ALS-XZ expert
    Rules out 4 from R2C5.
  9. Step 18 · Empty Rectangle advanced
    Rules out 4 from R4C9.
  10. Step 19 · W-Wing advanced
    Rules out 9 from R8C5.
  11. Step 20 · Nice Loops/AICs expert
    Rules out 4 from R4C1, R6C1.
  12. Step 22 · Nice Loops/AICs expert
    Rules out 6 from R8C5.
  13. Step 23 · WXYZ-Wing expert
    Rules out 7 from R8C4.
  14. Step 25 · Nice Loops/AICs expert
    Rules out 6 from R2C8.
  15. Step 26 · Finned Fish expert
    Rules out 6 from R6C9.
  16. Step 27 · Empty Rectangle advanced
    Rules out 6 from R7C2.
  17. Step 30 · ALS-XZ expert
    Rules out 9 from R1C7.
  18. Step 31 · ALS-XZ expert
    Rules out 9 from R8C4.
  19. Step 32 · Empty Rectangle advanced
    Rules out 9 from R6C7.
  20. Step 33 · Nice Loops/AICs expert
    Rules out 6 from R2C9, R3C4.
  21. Step 39 · XY-Chain expert
    Rules out 7 from R1C8, R2C1.

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.