EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 73: 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 73 of 150 in Extreme Sudoku 3
Difficulty
Expert 7 (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: Nice Loops/AICs (×4), ALS-XZ (×2), Finned Fish (×2), Skyscraper (×2), W-Wing (×2), 2-String Kite, Cell Forcing Chains, Empty Rectangle, Sue de Coq, 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 (23)
  1. Step 4 · Skyscraper advanced
    Rules out 4 from R5C2.
  2. Step 5 · 2-String Kite advanced
    Rules out 8 from R6C5.
  3. Step 8 · Finned Fish expert
    Rules out 9 from R9C1, R9C3.
  4. Step 9 · WXYZ-Wing expert
    Rules out 8 from R7C2, R9C2.
  5. Step 10 · ALS-XZ expert
    Rules out 8 from R7C1, R9C1.
  6. Step 11 · Nice Loops/AICs expert
    Rules out 5 from R7C8.
  7. Step 12 · Nice Loops/AICs expert
    Rules out 5 from R9C4.
  8. Step 13 · Nice Loops/AICs expert
    Rules out 6 from R9C7.
  9. Step 14 · Cell Forcing Chains expert
    Rules out 9 from R3C3.
  10. Step 18 · W-Wing advanced
    Rules out 7 from R7C6.
  11. Step 19 · XY-Chain expert
    Rules out 2 from R1C5.
  12. Step 21 · XY-Chain expert
    Rules out 5 from R5C5.
  13. Step 23 · Empty Rectangle advanced
    Rules out 5 from R9C8.
  14. Step 24 · Skyscraper advanced
    Rules out 5 from R4C7, R5C6.
  15. Step 26 · X-Wing/Swordfish advanced
    Rules out 4 from R9C2, R9C7.
  16. Step 27 · Finned Fish expert
    Rules out 5 from R9C9.
  17. Step 28 · XY-Chain expert
    Rules out 6 from R9C6.
  18. Step 29 · Sue de Coq expert
    Rules out 2 from R2C2; 7 from R9C1.
  19. Step 30 · ALS-XZ expert
    Rules out 1 from R9C7.
  20. Step 31 · Nice Loops/AICs expert
    Rules out 2 from R1C1.
  21. Step 32 · XY-Chain expert
    Rules out 7 from R2C1, R7C2, R9C2.
  22. Step 34 · XY-Chain expert
    Rules out 9 from R2C1, R3C4.
  23. Step 38 · W-Wing advanced
    Rules out 6 from R4C7.

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.