EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 87: 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 87 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
31 of 58 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 (×4), WXYZ-Wing (×3), XY-Wing (×3), Finned Fish (×2), XY-Chain (×2), Cell Forcing Chains, Empty Rectangle, W-Wing, 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 (24 of 31)
  1. Step 4 · Empty Rectangle advanced
    Rules out 3 from R2C2.
  2. Step 5 · WXYZ-Wing expert
    Rules out 2 from R6C5, R6C6.
  3. Step 6 · WXYZ-Wing expert
    Rules out 5 from R6C9.
  4. Step 7 · ALS-XZ expert
    Rules out 3 from R1C5.
  5. Step 8 · ALS-XZ expert
    Rules out 1 from R2C2, R2C3.
  6. Step 9 · ALS-XZ expert
    Rules out 7 from R2C3.
  7. Step 10 · ALS-XZ expert
    Rules out 4 from R5C9.
  8. Step 11 · Nice Loops/AICs expert
    Rules out 1 from R1C2.
  9. Step 13 · Nice Loops/AICs expert
    Rules out 5 from R4C9, R5C9.
  10. Step 16 · 2-String Kite advanced
    Rules out 5 from R7C5.
  11. Step 17 · Finned Fish expert
    Rules out 5 from R9C5.
  12. Step 19 · 2-String Kite advanced
    Rules out 3 from R2C5.
  13. Step 21 · 2-String Kite advanced
    Rules out 4 from R7C4.
  14. Step 22 · 2-String Kite advanced
    Rules out 4 from R2C5.
  15. Step 23 · Nice Loops/AICs expert
    Rules out 5 from R5C4.
  16. Step 25 · Nice Loops/AICs expert
    Rules out 4 from R4C5.
  17. Step 26 · Cell Forcing Chains expert
    Rules out 3 from R1C2.
  18. Step 28 · ALS-XZ expert
    Rules out 2 from R3C4.
  19. Step 29 · Nice Loops/AICs expert
    Rules out 3 from R3C4.
  20. Step 31 · XY-Wing advanced
    Rules out 5 from R8C3.
  21. Step 32 · XY-Wing advanced
    Rules out 7 from R1C5.
  22. Step 36 · Finned Fish expert
    Rules out 4 from R5C7.
  23. Step 38 · XY-Chain expert
    Rules out 3 from R8C2.
  24. Step 39 · WXYZ-Wing expert
    Rules out 6 from R2C6.

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.