EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 140: 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 140 of 150 in Extreme Sudoku 1
Difficulty
Expert 6 (expert and beyond), from the final, hardest third of the book
Key technique
Nice Loops/AICs
Hard steps
22 of 49 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), Finned Fish (×4), XY-Chain (×3), 2-String Kite, Cell Forcing Chains, Empty Rectangle, WXYZ-Wing, 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 (22)
  1. Step 6 · 2-String Kite advanced
    Rules out 5 from R1C8.
  2. Step 7 · XYZ-Wing advanced
    Rules out 2 from R6C7.
  3. Step 8 · Finned Fish expert
    Rules out 7 from R5C1.
  4. Step 9 · Finned Fish expert
    Rules out 7 from R6C2.
  5. Step 10 · ALS-XZ expert
    Rules out 1 from R5C5.
  6. Step 11 · ALS-XZ expert
    Rules out 6 from R1C6.
  7. Step 12 · ALS-XZ expert
    Rules out 7 from R5C3.
  8. Step 14 · Nice Loops/AICs expert
    Rules out 9 from R6C2.
  9. Step 16 · Cell Forcing Chains expert
    Rules out 1 from R1C6.
  10. Step 19 · Nice Loops/AICs expert
    Rules out 7 from R4C1.
  11. Step 20 · Nice Loops/AICs expert
    Rules out 7 from R7C1.
  12. Step 23 · Empty Rectangle advanced
    Rules out 1 from R5C1.
  13. Step 24 · WXYZ-Wing expert
    Rules out 2 from R4C3.
  14. Step 25 · Nice Loops/AICs expert
    Rules out 1 from R7C5.
  15. Step 26 · Nice Loops/AICs expert
    Rules out 2 from R7C5.
  16. Step 30 · XY-Wing advanced
    Rules out 4 from R4C2.
  17. Step 31 · ALS-XZ expert
    Rules out 1 from R9C2.
  18. Step 34 · Finned Fish expert
    Rules out 1 from R3C3.
  19. Step 37 · XY-Chain expert
    Rules out 2 from R8C5.
  20. Step 42 · Finned Fish expert
    Rules out 2 from R6C3.
  21. Step 43 · XY-Chain expert
    Rules out 7 from R1C7.
  22. Step 45 · XY-Chain expert
    Rules out 2 from R6C4.

The book

Classic 9×9 sudoku with the warm-up taken out. Every grid sits at the top of the expert range or beyond it, and the book ramps from hard to brutal.

150 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 Killer Sudoku 1 · Extreme Sudoku 2 · Extreme Killer Sudoku 2 · Extreme Sudoku 3 · Extreme Killer Sudoku 3.