EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 40: 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 40 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
22 of 41 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 (×6), Nice Loops/AICs (×2), 2-String Kite, Cell Forcing Chains, Finned Fish, W-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 (22)
  1. Step 4 · 2-String Kite advanced
    Rules out 5 from R5C5.
  2. Step 5 · Finned Fish expert
    Rules out 5 from R8C2.
  3. Step 6 · XY-Chain expert
    Rules out 3 from R5C7, R6C4, R6C5.
  4. Step 8 · ALS-XZ expert
    Rules out 8 from R2C3.
  5. Step 9 · ALS-XZ expert
    Rules out 7 from R9C3.
  6. Step 10 · ALS-XZ expert
    Rules out 9 from R4C2.
  7. Step 11 · ALS-XZ expert
    Rules out 9 from R4C7.
  8. Step 13 · ALS-XZ expert
    Rules out 9 from R2C3.
  9. Step 14 · ALS-XZ expert
    Rules out 8 from R1C5.
  10. Step 15 · Nice Loops/AICs expert
    Rules out 1 from R8C3.
  11. Step 16 · Nice Loops/AICs expert
    Rules out 5 from R4C5.
  12. Step 17 · Cell Forcing Chains expert
    Rules out 8 from R1C3.
  13. Step 19 · XY-Chain expert
    Rules out 5 from R8C1.
  14. Step 21 · XY-Chain expert
    Rules out 7 from R4C3.
  15. Step 22 · XY-Chain expert
    Rules out 2 from R4C9, R6C5.
  16. Step 25 · XY-Chain expert
    Rules out 5 from R4C2.
  17. Step 26 · XY-Chain expert
    Rules out 8 from R2C2.
  18. Step 32 · XY-Chain expert
    Rules out 9 from R2C7.
  19. Step 33 · XY-Chain expert
    Rules out 2 from R2C8, R3C1.
  20. Step 35 · XY-Chain expert
    Rules out 3 from R9C2.
  21. Step 36 · XY-Chain expert
    Rules out 9 from R2C1.
  22. Step 37 · W-Wing advanced
    Rules out 8 from R2C6.

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.