EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 6: 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 6 of 150 in Extreme Sudoku 3
Difficulty
Expert 5 (expert and beyond), from the opening third of the book
Key technique
XY-Chain
Hard steps
20 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 (×4), 2-String Kite (×2), Nice Loops/AICs (×2), Empty Rectangle, Finned Fish, Skyscraper, WXYZ-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 (20)
  1. Step 4 · Skyscraper advanced
    Rules out 2 from R1C2, R5C3.
  2. Step 5 · Empty Rectangle advanced
    Rules out 5 from R5C5.
  3. Step 6 · ALS-XZ expert
    Rules out 9 from R5C9.
  4. Step 7 · ALS-XZ expert
    Rules out 9 from R5C8.
  5. Step 9 · Nice Loops/AICs expert
    Rules out 4 from R6C2.
  6. Step 11 · 2-String Kite advanced
    Rules out 5 from R9C6.
  7. Step 13 · WXYZ-Wing expert
    Rules out 3 from R9C4.
  8. Step 14 · ALS-XZ expert
    Rules out 2 from R6C6.
  9. Step 19 · X-Wing/Swordfish advanced
    Rules out 6 from R1C2, R1C9, R3C3, R8C2 and 2 more.
  10. Step 21 · ALS-XZ expert
    Rules out 6 from R9C2.
  11. Step 22 · Nice Loops/AICs expert
    Rules out 7 from R1C1.
  12. Step 23 · XY-Chain expert
    Rules out 7 from R4C2.
  13. Step 25 · 2-String Kite advanced
    Rules out 7 from R9C7.
  14. Step 31 · XY-Chain expert
    Rules out 6 from R1C4.
  15. Step 32 · XY-Chain expert
    Rules out 3 from R4C3, R8C2.
  16. Step 34 · XY-Chain expert
    Rules out 1 from R7C8.
  17. Step 35 · Finned Fish expert
    Rules out 1 from R5C7, R5C9.
  18. Step 36 · XY-Chain expert
    Rules out 1 from R8C8.
  19. Step 38 · XY-Chain expert
    Rules out 6 from R2C2.
  20. Step 41 · XY-Chain expert
    Rules out 6 from R8C1.

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.