EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 78: 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 78 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 46 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 (×5), Finned Fish (×4), ALS-XZ (×2), 2-String Kite, Cell Forcing Chains, Sue de Coq, W-Wing, WXYZ-Wing, XYZ-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 (23)
  1. Step 4 · XYZ-Wing advanced
    Rules out 9 from R5C5.
  2. Step 5 · Nice Loops/AICs expert
    Rules out 6 from R9C4.
  3. Step 6 · Cell Forcing Chains expert
    Rules out 4 from R1C9.
  4. Step 8 · Nice Loops/AICs expert
    Rules out 6 from R7C4.
  5. Step 10 · 2-String Kite advanced
    Rules out 7 from R2C5.
  6. Step 11 · Finned Fish expert
    Rules out 7 from R7C5.
  7. Step 12 · Finned Fish expert
    Rules out 7 from R2C2.
  8. Step 13 · Nice Loops/AICs expert
    Rules out 7 from R3C8.
  9. Step 14 · WXYZ-Wing expert
    Rules out 7 from R2C3.
  10. Step 15 · Finned Fish expert
    Rules out 7 from R1C8.
  11. Step 20 · W-Wing advanced
    Rules out 7 from R4C5, R5C8.
  12. Step 22 · Finned Fish expert
    Rules out 7 from R7C4.
  13. Step 24 · Sue de Coq expert
    Rules out 9 from R8C5, R8C6.
  14. Step 25 · ALS-XZ expert
    Rules out 6 from R1C1.
  15. Step 26 · ALS-XZ expert
    Rules out 9 from R8C1.
  16. Step 27 · Nice Loops/AICs expert
    Rules out 8 from R6C6.
  17. Step 28 · Nice Loops/AICs expert
    Rules out 7 from R8C2.
  18. Step 31 · XY-Chain expert
    Rules out 5 from R4C2.
  19. Step 33 · XY-Chain expert
    Rules out 4 from R8C8.
  20. Step 34 · XY-Chain expert
    Rules out 4 from R3C8.
  21. Step 35 · XY-Chain expert
    Rules out 8 from R5C8.
  22. Step 38 · XY-Chain expert
    Rules out 4 from R9C1.
  23. Step 40 · XY-Chain expert
    Rules out 8 from R4C9.

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.