EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 58: 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 58 of 150 in Extreme Sudoku 2
Difficulty
Expert 6 (expert and beyond), from the middle 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: W-Wing (×3), XY-Chain (×3), WXYZ-Wing (×2), XY-Wing (×2), 2-String Kite, ALS-XZ, Cell Forcing Chains, Empty Rectangle, Finned Fish, X-Wing/Swordfish.

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 7 · Empty Rectangle advanced
    Rules out 5 from R9C2.
  2. Step 8 · W-Wing advanced
    Rules out 3 from R5C4.
  3. Step 9 · XY-Wing advanced
    Rules out 9 from R5C2.
  4. Step 10 · WXYZ-Wing expert
    Rules out 9 from R6C6.
  5. Step 11 · ALS-XZ expert
    Rules out 8 from R5C8.
  6. Step 12 · Nice Loops/AICs expert
    Rules out 7 from R7C1.
  7. Step 14 · WXYZ-Wing expert
    Rules out 7 from R1C6.
  8. Step 16 · Nice Loops/AICs expert
    Rules out 3 from R2C6.
  9. Step 17 · Nice Loops/AICs expert
    Rules out 4 from R2C4.
  10. Step 23 · XY-Chain expert
    Rules out 9 from R5C7.
  11. Step 24 · Cell Forcing Chains expert
    Rules out 1 from R1C1.
  12. Step 28 · W-Wing advanced
    Rules out 5 from R5C7.
  13. Step 30 · Finned Fish expert
    Rules out 9 from R4C2.
  14. Step 31 · W-Wing advanced
    Rules out 5 from R4C1, R7C2.
  15. Step 32 · XY-Chain expert
    Rules out 5 from R7C8.
  16. Step 35 · 2-String Kite advanced
    Rules out 1 from R6C2.
  17. Step 36 · X-Wing/Swordfish advanced
    Rules out 1 from R4C1.
  18. Step 37 · XY-Wing advanced
    Rules out 9 from R6C9.
  19. Step 41 · XY-Chain expert
    Rules out 1 from R6C1, R7C2.

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.