EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 86: 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 86 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
23 of 51 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 (×6), 2-String Kite (×2), XY-Chain (×2), Cell Forcing Chains, Empty Rectangle, Finned Fish, W-Wing, WXYZ-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 (23)
  1. Step 7 · 2-String Kite advanced
    Rules out 4 from R9C9.
  2. Step 8 · ALS-XZ expert
    Rules out 3 from R9C4.
  3. Step 9 · ALS-XZ expert
    Rules out 6 from R2C5.
  4. Step 10 · Nice Loops/AICs expert
    Rules out 4 from R9C3.
  5. Step 11 · Nice Loops/AICs expert
    Rules out 1 from R7C6.
  6. Step 12 · Finned Fish expert
    Rules out 1 from R6C2.
  7. Step 13 · ALS-XZ expert
    Rules out 6 from R4C3.
  8. Step 14 · Nice Loops/AICs expert
    Rules out 5 from R9C8.
  9. Step 16 · Nice Loops/AICs expert
    Rules out 4 from R9C6.
  10. Step 17 · ALS-XZ expert
    Rules out 1 from R8C6.
  11. Step 18 · W-Wing advanced
    Rules out 6 from R9C5.
  12. Step 19 · ALS-XZ expert
    Rules out 1 from R9C5.
  13. Step 20 · Nice Loops/AICs expert
    Rules out 9 from R9C1.
  14. Step 21 · Nice Loops/AICs expert
    Rules out 2 from R4C3.
  15. Step 22 · XYZ-Wing advanced
    Rules out 4 from R4C1.
  16. Step 25 · ALS-XZ expert
    Rules out 4 from R5C9.
  17. Step 28 · Cell Forcing Chains expert
    Rules out 9 from R2C5.
  18. Step 31 · 2-String Kite advanced
    Rules out 6 from R7C4.
  19. Step 33 · WXYZ-Wing expert
    Rules out 1 from R8C5.
  20. Step 34 · Nice Loops/AICs expert
    Rules out 1 from R4C5.
  21. Step 41 · Empty Rectangle advanced
    Rules out 6 from R1C3.
  22. Step 44 · XY-Chain expert
    Rules out 6 from R7C7.
  23. Step 47 · XY-Chain expert
    Rules out 1 from R2C9, R9C8.

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.