EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 91: 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 91 of 150 in Extreme Sudoku 3
Difficulty
Expert 5 (expert and beyond), from the middle third of the book
Key technique
ALS-XZ
Hard steps
18 of 38 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: ALS-XZ

Two almost-locked sets (n cells with n+1 candidates) share a restricted digit X. Then a digit Z common to both must be in one of them, so cells seeing all of its copies cannot be Z.

Other advanced and expert techniques in this solve: XY-Chain (×4), Nice Loops/AICs (×3), Finned Fish (×2), Cell Forcing Chains, Empty Rectangle, W-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 (18)
  1. Step 8 · ALS-XZ expert
    Rules out 3 from R9C5.
  2. Step 9 · ALS-XZ expert
    Rules out 1 from R8C6, R9C6.
  3. Step 10 · Nice Loops/AICs expert
    Rules out 6 from R1C4.
  4. Step 11 · Nice Loops/AICs expert
    Rules out 9 from R8C7.
  5. Step 12 · Nice Loops/AICs expert
    Rules out 2 from R7C9; 4 from R7C9; 6 from R7C9.
  6. Step 13 · Finned Fish expert
    Rules out 6 from R8C6, R9C6.
  7. Step 14 · ALS-XZ expert
    Rules out 7 from R8C6, R9C7.
  8. Step 16 · Empty Rectangle advanced
    Rules out 1 from R4C9.
  9. Step 17 · Cell Forcing Chains expert
    Rules out 1 from R1C4.
  10. Step 20 · X-Wing/Swordfish advanced
    Rules out 6 from R2C6, R9C2.
  11. Step 21 · Finned Fish expert
    Rules out 2 from R8C9, R9C9.
  12. Step 23 · ALS-XZ expert
    Rules out 6 from R9C5.
  13. Step 24 · ALS-XZ expert
    Rules out 5 from R5C6, R8C4.
  14. Step 26 · XY-Chain expert
    Rules out 4 from R9C9.
  15. Step 27 · W-Wing advanced
    Rules out 9 from R6C7.
  16. Step 30 · XY-Chain expert
    Rules out 5 from R4C9, R5C2.
  17. Step 32 · XY-Chain expert
    Rules out 2 from R7C2.
  18. Step 33 · XY-Chain expert
    Rules out 1 from R4C7, R6C3.

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.