EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 16: 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 16 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
16 of 37 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 (×4), Finned Fish (×2), WXYZ-Wing (×2), Nice Loops/AICs, X-Wing/Swordfish, 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 (16)
  1. Step 8 · WXYZ-Wing expert
    Rules out 5 from R4C7.
  2. Step 9 · ALS-XZ expert
    Rules out 2 from R4C1.
  3. Step 11 · Finned Fish expert
    Rules out 7 from R4C4.
  4. Step 12 · Finned Fish expert
    Rules out 5 from R1C8.
  5. Step 13 · XY-Chain expert
    Rules out 4 from R2C9.
  6. Step 14 · XY-Chain expert
    Rules out 9 from R4C4, R4C5, R5C2.
  7. Step 15 · WXYZ-Wing expert
    Rules out 5 from R7C7, R7C8.
  8. Step 17 · XYZ-Wing advanced
    Rules out 9 from R8C8.
  9. Step 19 · ALS-XZ expert
    Rules out 4 from R1C8.
  10. Step 20 · ALS-XZ expert
    Rules out 7 from R7C4.
  11. Step 21 · ALS-XZ expert
    Rules out 1 from R4C1.
  12. Step 23 · Nice Loops/AICs expert
    Rules out 4 from R2C8.
  13. Step 27 · X-Wing/Swordfish advanced
    Rules out 5 from R5C4, R5C5, R9C4.
  14. Step 28 · XY-Chain expert
    Rules out 3 from R2C4.
  15. Step 30 · XY-Chain expert
    Rules out 5 from R1C7.
  16. Step 32 · XY-Chain expert
    Rules out 5 from R7C3.

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.