EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 84: 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 84 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
23 of 42 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 (×5), XY-Wing (×3), 2-String Kite (×2), Finned Fish (×2), Nice Loops/AICs (×2), XYZ-Wing (×2), Cell Forcing Chains.

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 6 · 2-String Kite advanced
    Rules out 2 from R7C5.
  2. Step 7 · Finned Fish expert
    Rules out 3 from R5C1.
  3. Step 8 · ALS-XZ expert
    Rules out 9 from R2C1.
  4. Step 9 · XYZ-Wing advanced
    Rules out 7 from R6C1.
  5. Step 10 · ALS-XZ expert
    Rules out 5 from R8C8.
  6. Step 11 · Cell Forcing Chains expert
    Rules out 8 from R1C1.
  7. Step 14 · Nice Loops/AICs expert
    Rules out 3 from R5C3.
  8. Step 15 · Finned Fish expert
    Rules out 3 from R6C8.
  9. Step 16 · Nice Loops/AICs expert
    Rules out 4 from R5C7.
  10. Step 18 · ALS-XZ expert
    Rules out 2 from R8C8.
  11. Step 19 · ALS-XZ expert
    Rules out 9 from R6C8.
  12. Step 20 · ALS-XZ expert
    Rules out 7 from R4C1.
  13. Step 21 · XY-Wing advanced
    Rules out 7 from R2C2.
  14. Step 23 · XY-Chain expert
    Rules out 9 from R3C1.
  15. Step 27 · XYZ-Wing advanced
    Rules out 5 from R8C9.
  16. Step 28 · XY-Chain expert
    Rules out 7 from R2C3.
  17. Step 30 · 2-String Kite advanced
    Rules out 7 from R8C8.
  18. Step 31 · XY-Wing advanced
    Rules out 2 from R8C5.
  19. Step 32 · XY-Chain expert
    Rules out 2 from R2C8.
  20. Step 33 · XY-Chain expert
    Rules out 2 from R5C8, R7C8, R9C8.
  21. Step 34 · XY-Wing advanced
    Rules out 5 from R2C8.
  22. Step 35 · XY-Chain expert
    Rules out 9 from R2C8.
  23. Step 40 · XY-Chain expert
    Rules out 3 from R2C4, R3C1.

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.