EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 89: 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 89 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
12 of 29 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 (×2), Cell Forcing Chains, Nice Loops/AICs, Sue de Coq, W-Wing, 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 (12)
  1. Step 7 · ALS-XZ expert
    Rules out 3 from R1C4.
  2. Step 9 · ALS-XZ expert
    Rules out 3 from R1C2.
  3. Step 11 · XYZ-Wing advanced
    Rules out 9 from R9C8.
  4. Step 12 · ALS-XZ expert
    Rules out 9 from R3C4.
  5. Step 13 · Nice Loops/AICs expert
    Rules out 6 from R9C4.
  6. Step 14 · Cell Forcing Chains expert
    Rules out 6 from R1C1, R4C1, R7C8; 9 from R1C7, R3C5, R4C8, R6C6 and 1 more; 1 from R3C3.
  7. Step 17 · Sue de Coq expert
    Rules out 9 from R8C4, R9C4.
  8. Step 18 · ALS-XZ expert
    Rules out 9 from R6C2.
  9. Step 19 · ALS-XZ expert
    Rules out 9 from R4C2.
  10. Step 20 · W-Wing advanced
    Rules out 6 from R5C7.
  11. Step 24 · XY-Chain expert
    Rules out 9 from R4C9.
  12. Step 26 · XY-Chain expert
    Rules out 4 from R4C5.

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.