EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 108: 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 108 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
20 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: 2-String Kite (×3), ALS-XZ (×2), Cell Forcing Chains, Empty Rectangle, Finned Fish, WXYZ-Wing, XY-Chain, 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 4 · Empty Rectangle advanced
    Rules out 8 from R8C5.
  2. Step 5 · Finned Fish expert
    Rules out 7 from R6C1.
  3. Step 6 · WXYZ-Wing expert
    Rules out 9 from R6C6.
  4. Step 7 · Nice Loops/AICs expert
    Rules out 7 from R2C2.
  5. Step 8 · Nice Loops/AICs expert
    Rules out 7 from R2C3.
  6. Step 10 · Nice Loops/AICs expert
    Rules out 7 from R5C4.
  7. Step 14 · XY-Chain expert
    Rules out 8 from R1C8.
  8. Step 15 · ALS-XZ expert
    Rules out 7 from R6C4.
  9. Step 16 · Nice Loops/AICs expert
    Rules out 3 from R8C2.
  10. Step 17 · Nice Loops/AICs expert
    Rules out 8 from R9C7.
  11. Step 19 · Nice Loops/AICs expert
    Rules out 8 from R3C8, R8C7.
  12. Step 21 · Nice Loops/AICs expert
    Rules out 5 from R9C7.
  13. Step 22 · Cell Forcing Chains expert
    Rules out 9 from R1C9.
  14. Step 27 · 2-String Kite advanced
    Rules out 1 from R4C3.
  15. Step 29 · ALS-XZ expert
    Rules out 6 from R3C8.
  16. Step 30 · Nice Loops/AICs expert
    Rules out 4 from R6C3.
  17. Step 31 · 2-String Kite advanced
    Rules out 4 from R4C4.
  18. Step 34 · Nice Loops/AICs expert
    Rules out 1 from R7C9, R8C3.
  19. Step 39 · 2-String Kite advanced
    Rules out 9 from R2C7.
  20. Step 40 · XY-Wing advanced
    Rules out 9 from R2C5.

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.