EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 77: 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 77 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
24 of 54 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 (×3), 2-String Kite (×2), Cell Forcing Chains, Empty Rectangle, Finned Fish, Skyscraper, Sue de Coq, 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)
  1. Step 6 · Skyscraper advanced
    Rules out 5 from R3C1.
  2. Step 8 · ALS-XZ expert
    Rules out 7 from R6C4.
  3. Step 9 · ALS-XZ expert
    Rules out 6 from R4C6.
  4. Step 10 · Nice Loops/AICs expert
    Rules out 9 from R2C8.
  5. Step 12 · Nice Loops/AICs expert
    Rules out 6 from R5C8.
  6. Step 13 · Nice Loops/AICs expert
    Rules out 6 from R4C3.
  7. Step 15 · Nice Loops/AICs expert
    Rules out 7 from R9C7.
  8. Step 16 · Cell Forcing Chains expert
    Rules out 7 from R2C3.
  9. Step 19 · Empty Rectangle advanced
    Rules out 7 from R6C5.
  10. Step 20 · Finned Fish expert
    Rules out 7 from R9C8.
  11. Step 21 · XY-Chain expert
    Rules out 9 from R5C4, R7C6.
  12. Step 24 · XY-Chain expert
    Rules out 6 from R5C4, R5C5, R6C2.
  13. Step 25 · WXYZ-Wing expert
    Rules out 6 from R6C4.
  14. Step 26 · Sue de Coq expert
    Rules out 7 from R8C5, R9C5.
  15. Step 28 · ALS-XZ expert
    Rules out 7 from R7C4.
  16. Step 31 · 2-String Kite advanced
    Rules out 1 from R6C8.
  17. Step 32 · XY-Chain expert
    Rules out 2 from R8C7, R8C8.
  18. Step 36 · XY-Chain expert
    Rules out 1 from R3C3.
  19. Step 37 · XY-Chain expert
    Rules out 1 from R4C8.
  20. Step 39 · XY-Chain expert
    Rules out 7 from R1C3.
  21. Step 40 · 2-String Kite advanced
    Rules out 7 from R3C4.
  22. Step 41 · XY-Chain expert
    Rules out 8 from R5C2.
  23. Step 43 · XY-Chain expert
    Rules out 5 from R6C2.
  24. Step 48 · XY-Wing advanced
    Rules out 7 from R5C4.

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.