EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, 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 3
Difficulty
Expert 5 (expert and beyond), from the middle third of the book
Key technique
XY-Chain
Hard steps
26 of 47 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: XY-Chain

A chain of two-candidate cells, each linked to the next. Whichever way the start cell goes, one end of the chain holds the digit, so cells seeing both ends cannot.

Other advanced and expert techniques in this solve: ALS-XZ (×7), Nice Loops/AICs (×2), Finned Fish, Skyscraper, W-Wing, 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 of 26)
  1. Step 5 · Finned Fish expert
    Rules out 6 from R7C1.
  2. Step 6 · ALS-XZ expert
    Rules out 2 from R6C4, R8C5.
  3. Step 7 · ALS-XZ expert
    Rules out 8 from R8C4.
  4. Step 8 · ALS-XZ expert
    Rules out 8 from R5C5.
  5. Step 9 · ALS-XZ expert
    Rules out 3 from R1C6.
  6. Step 10 · ALS-XZ expert
    Rules out 9 from R3C6.
  7. Step 11 · XY-Chain expert
    Rules out 3 from R1C4.
  8. Step 12 · XY-Chain expert
    Rules out 9 from R2C3.
  9. Step 13 · XY-Chain expert
    Rules out 4 from R3C5.
  10. Step 14 · XY-Chain expert
    Rules out 5 from R2C7.
  11. Step 16 · XY-Chain expert
    Rules out 6 from R3C9.
  12. Step 20 · W-Wing advanced
    Rules out 2 from R8C3.
  13. Step 21 · XY-Chain expert
    Rules out 3 from R3C1, R3C2.
  14. Step 22 · XY-Wing advanced
    Rules out 2 from R4C2, R6C2.
  15. Step 23 · WXYZ-Wing expert
    Rules out 9 from R7C3.
  16. Step 24 · ALS-XZ expert
    Rules out 2 from R9C2.
  17. Step 26 · Nice Loops/AICs expert
    Rules out 3 from R7C3.
  18. Step 27 · Nice Loops/AICs expert
    Rules out 3 from R8C3.
  19. Step 28 · XY-Chain expert
    Rules out 9 from R1C3, R7C1, R8C1.
  20. Step 31 · Skyscraper advanced
    Rules out 3 from R1C1.
  21. Step 32 · XY-Chain expert
    Rules out 8 from R6C6.
  22. Step 33 · XY-Chain expert
    Rules out 9 from R1C4.
  23. Step 34 · ALS-XZ expert
    Rules out 8 from R6C2.
  24. Step 37 · XY-Chain expert
    Rules out 5 from R1C1, R7C2.

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.