EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 72: 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 72 of 150 in Extreme Sudoku 3
Difficulty
Expert 7 (expert and beyond), from the middle third of the book
Key technique
ALS-XZ
Hard steps
25 of 46 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: Nice Loops/AICs (×6), Empty Rectangle (×2), XY-Chain (×2), Cell Forcing Chains, Finned Fish, Sue de Coq, W-Wing, WXYZ-Wing, XY-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 (24 of 25)
  1. Step 4 · W-Wing advanced
    Rules out 7 from R5C9, R6C9.
  2. Step 5 · Nice Loops/AICs expert
    Rules out 2 from R2C3.
  3. Step 6 · Nice Loops/AICs expert
    Rules out 2 from R2C4, R2C5, R3C4.
  4. Step 7 · Nice Loops/AICs expert
    Rules out 4 from R8C9.
  5. Step 8 · Nice Loops/AICs expert
    Rules out 7 from R2C3.
  6. Step 9 · Nice Loops/AICs expert
    Rules out 9 from R4C1, R4C2.
  7. Step 10 · Cell Forcing Chains expert
    Rules out 2 from R2C1, R3C7, R8C3; 5 from R2C7, R3C4, R3C6; 6 from R4C4, R6C4.
  8. Step 12 · Empty Rectangle advanced
    Rules out 5 from R9C9.
  9. Step 13 · ALS-XZ expert
    Rules out 5 from R7C4, R7C5.
  10. Step 14 · ALS-XZ expert
    Rules out 6 from R8C5.
  11. Step 15 · ALS-XZ expert
    Rules out 2 from R7C1, R8C5.
  12. Step 17 · Empty Rectangle advanced
    Rules out 7 from R6C3.
  13. Step 18 · XYZ-Wing advanced
    Rules out 6 from R9C3.
  14. Step 19 · ALS-XZ expert
    Rules out 4 from R4C3.
  15. Step 20 · ALS-XZ expert
    Rules out 4 from R8C8.
  16. Step 21 · WXYZ-Wing expert
    Rules out 4 from R7C2.
  17. Step 22 · Nice Loops/AICs expert
    Rules out 4 from R6C9.
  18. Step 23 · Finned Fish expert
    Rules out 4 from R5C5.
  19. Step 24 · ALS-XZ expert
    Rules out 4 from R7C4.
  20. Step 26 · Sue de Coq expert
    Rules out 2 from R5C4.
  21. Step 27 · ALS-XZ expert
    Rules out 4 from R8C3.
  22. Step 31 · ALS-XZ expert
    Rules out 7 from R5C2.
  23. Step 35 · XY-Chain expert
    Rules out 3 from R4C1.
  24. Step 39 · XY-Wing advanced
    Rules out 7 from R2C4.

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.