EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 115: 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 115 of 150 in Extreme Sudoku 3
Difficulty
Expert 7 (expert and beyond), from the final, hardest third of the book
Key technique
XY-Chain
Hard steps
14 of 33 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: XY-Wing (×2), ALS-XZ, Cell Forcing Chains, Empty Rectangle, Finned Fish, Nice Loops/AICs, Sue de Coq, W-Wing, 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 (14)
  1. Step 5 · XY-Wing advanced
    Rules out 6 from R5C4, R5C5, R5C6.
  2. Step 7 · Empty Rectangle advanced
    Rules out 6 from R4C7.
  3. Step 8 · WXYZ-Wing expert
    Rules out 9 from R1C5, R2C3.
  4. Step 10 · Sue de Coq expert
    Rules out 1 from R6C9; 7 from R6C9.
  5. Step 11 · ALS-XZ expert
    Rules out 6 from R1C5.
  6. Step 14 · Nice Loops/AICs expert
    Rules out 6 from R5C7.
  7. Step 15 · Cell Forcing Chains expert
    Rules out 4 from R1C2.
  8. Step 20 · W-Wing advanced
    Rules out 1 from R5C1.
  9. Step 22 · Finned Fish expert
    Rules out 1 from R4C8, R4C9.
  10. Step 23 · XY-Chain expert
    Rules out 4 from R1C7.
  11. Step 26 · XY-Chain expert
    Rules out 4 from R8C7.
  12. Step 28 · X-Wing/Swordfish advanced
    Rules out 1 from R4C2, R8C3, R8C8, R8C9.
  13. Step 29 · XY-Wing advanced
    Rules out 1 from R9C8.
  14. Step 31 · XY-Chain expert
    Rules out 1 from R2C2.

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.