EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 51: 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 51 of 150 in Extreme Sudoku 3
Difficulty
Expert 6 (expert and beyond), from the middle third of the book
Key technique
XY-Chain
Hard steps
17 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: 2-String Kite (×3), XY-Wing (×2), ALS-XZ, Finned Fish, Nice Loops/AICs, Sue de Coq, WXYZ-Wing, X-Wing/Swordfish.

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 (17)
  1. Step 4 · 2-String Kite advanced
    Rules out 1 from R9C7.
  2. Step 5 · 2-String Kite advanced
    Rules out 6 from R2C2.
  3. Step 8 · Finned Fish expert
    Rules out 1 from R9C9.
  4. Step 9 · WXYZ-Wing expert
    Rules out 7 from R5C5, R5C6.
  5. Step 10 · Sue de Coq expert
    Rules out 9 from R7C1, R8C8, R9C7, R9C8; 3 from R9C8.
  6. Step 11 · XY-Chain expert
    Rules out 2 from R8C4.
  7. Step 12 · XY-Chain expert
    Rules out 9 from R3C5, R9C6.
  8. Step 14 · XY-Wing advanced
    Rules out 3 from R4C1, R6C1, R9C2.
  9. Step 16 · XY-Chain expert
    Rules out 9 from R3C4.
  10. Step 20 · 2-String Kite advanced
    Rules out 2 from R5C8.
  11. Step 21 · XY-Chain expert
    Rules out 5 from R7C8.
  12. Step 22 · ALS-XZ expert
    Rules out 2 from R4C5.
  13. Step 23 · Nice Loops/AICs expert
    Rules out 2 from R4C8.
  14. Step 26 · XY-Chain expert
    Rules out 5 from R5C7, R6C7, R9C8.
  15. Step 29 · X-Wing/Swordfish advanced
    Rules out 1 from R1C4.
  16. Step 31 · XY-Chain expert
    Rules out 6 from R1C1, R5C3.
  17. Step 36 · XY-Wing advanced
    Rules out 1 from R7C9.

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.