EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 91: 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 91 of 150 in Extreme Sudoku 1
Difficulty
Expert 6 (expert and beyond), from the middle third of the book
Key technique
Nice Loops/AICs
Hard steps
24 of 48 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), Empty Rectangle (×4), XY-Chain (×4), 2-String Kite (×2), Finned Fish (×2), Cell Forcing Chains, WXYZ-Wing, 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 (24)
  1. Step 5 · 2-String Kite advanced
    Rules out 8 from R8C9.
  2. Step 6 · Finned Fish expert
    Rules out 8 from R9C9.
  3. Step 7 · Nice Loops/AICs expert
    Rules out 5 from R4C2, R5C2.
  4. Step 9 · WXYZ-Wing expert
    Rules out 4 from R6C1.
  5. Step 10 · Empty Rectangle advanced
    Rules out 4 from R4C6.
  6. Step 11 · Nice Loops/AICs expert
    Rules out 9 from R9C6.
  7. Step 12 · ALS-XZ expert
    Rules out 3 from R7C2.
  8. Step 13 · Nice Loops/AICs expert
    Rules out 2 from R7C2.
  9. Step 14 · Nice Loops/AICs expert
    Rules out 4 from R5C9.
  10. Step 15 · Finned Fish expert
    Rules out 4 from R6C6.
  11. Step 18 · Empty Rectangle advanced
    Rules out 9 from R8C9.
  12. Step 19 · Nice Loops/AICs expert
    Rules out 2 from R9C4.
  13. Step 21 · Cell Forcing Chains expert
    Rules out 4 from R2C2.
  14. Step 26 · ALS-XZ expert
    Rules out 6 from R9C3, R9C6, R9C9.
  15. Step 29 · XY-Chain expert
    Rules out 1 from R4C3.
  16. Step 30 · ALS-XZ expert
    Rules out 1 from R4C2.
  17. Step 33 · ALS-XZ expert
    Rules out 9 from R5C4.
  18. Step 34 · Empty Rectangle advanced
    Rules out 9 from R3C9.
  19. Step 35 · XY-Chain expert
    Rules out 5 from R6C4.
  20. Step 37 · Empty Rectangle advanced
    Rules out 2 from R9C7.
  21. Step 38 · XY-Wing advanced
    Rules out 4 from R6C7.
  22. Step 39 · XY-Chain expert
    Rules out 2 from R4C2, R6C1.
  23. Step 41 · 2-String Kite advanced
    Rules out 8 from R7C8.
  24. Step 42 · XY-Chain expert
    Rules out 9 from R4C7, R4C8, R4C9, R5C5.

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.