EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, 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 3
Difficulty
Expert 5 (expert and beyond), from the middle third of the book
Key technique
Nice Loops/AICs
Hard steps
18 of 46 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 (×2), W-Wing (×2), Cell Forcing Chains, 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 (18)
  1. Step 7 · ALS-XZ expert
    Rules out 7 from R1C1.
  2. Step 8 · Nice Loops/AICs expert
    Rules out 9 from R5C9.
  3. Step 10 · Cell Forcing Chains expert
    Rules out 1 from R2C8.
  4. Step 14 · Nice Loops/AICs expert
    Rules out 4 from R3C4.
  5. Step 15 · Nice Loops/AICs expert
    Rules out 2 from R1C7.
  6. Step 16 · Nice Loops/AICs expert
    Rules out 3 from R8C7.
  7. Step 17 · Nice Loops/AICs expert
    Rules out 4 from R3C3.
  8. Step 18 · W-Wing advanced
    Rules out 8 from R7C2, R8C2.
  9. Step 19 · Nice Loops/AICs expert
    Rules out 8 from R3C4.
  10. Step 20 · Nice Loops/AICs expert
    Rules out 4 from R4C5.
  11. Step 21 · Finned Fish expert
    Rules out 4 from R9C3.
  12. Step 25 · ALS-XZ expert
    Rules out 4 from R3C1.
  13. Step 26 · ALS-XZ expert
    Rules out 8 from R8C9.
  14. Step 31 · W-Wing advanced
    Rules out 5 from R1C6.
  15. Step 32 · ALS-XZ expert
    Rules out 5 from R1C9.
  16. Step 36 · XY-Chain expert
    Rules out 7 from R2C2.
  17. Step 38 · XY-Wing advanced
    Rules out 7 from R8C5.
  18. Step 41 · Finned Fish expert
    Rules out 4 from R7C4.

The book

Volume three: 150 new classic 9×9 grids, none repeated from books 1 or 2, 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.

On Amazon from 8 Dec About the book

Try a free sample puzzle (PDF) · prints on A4 or US Letter

More step-by-step solutions: Extreme Sudoku 1 · Extreme Killer Sudoku 1 · Extreme Sudoku 2 · Extreme Killer Sudoku 2 · Extreme Killer Sudoku 3.