EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 109: 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 109 of 150 in Extreme Sudoku 3
Difficulty
Expert 6 (expert and beyond), from the final, hardest third of the book
Key technique
XY-Chain
Hard steps
16 of 39 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: Finned Fish (×3), Nice Loops/AICs (×3), ALS-XZ, Cell Forcing Chains, W-Wing, WXYZ-Wing, X-Wing/Swordfish, 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 (16)
  1. Step 6 · Finned Fish expert
    Rules out 6 from R2C7.
  2. Step 7 · ALS-XZ expert
    Rules out 4 from R2C4.
  3. Step 8 · Nice Loops/AICs expert
    Rules out 1 from R2C9.
  4. Step 9 · Nice Loops/AICs expert
    Rules out 1 from R2C7.
  5. Step 11 · Nice Loops/AICs expert
    Rules out 6 from R6C8.
  6. Step 12 · Cell Forcing Chains expert
    Rules out 5 from R6C8.
  7. Step 13 · Finned Fish expert
    Rules out 5 from R9C5.
  8. Step 14 · XY-Wing advanced
    Rules out 1 from R2C5.
  9. Step 15 · XY-Chain expert
    Rules out 1 from R2C4.
  10. Step 20 · Finned Fish expert
    Rules out 9 from R1C9.
  11. Step 21 · XY-Chain expert
    Rules out 2 from R2C1.
  12. Step 24 · W-Wing advanced
    Rules out 9 from R9C7.
  13. Step 25 · WXYZ-Wing expert
    Rules out 9 from R6C7.
  14. Step 28 · X-Wing/Swordfish advanced
    Rules out 6 from R4C8, R9C8.
  15. Step 33 · XY-Chain expert
    Rules out 9 from R9C4.
  16. Step 34 · XY-Chain expert
    Rules out 9 from R1C4.

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.