EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 138: 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 138 of 150 in Extreme Sudoku 3
Difficulty
Expert 6 (expert and beyond), from the final, hardest third of the book
Key technique
ALS-XZ
Hard steps
16 of 39 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: WXYZ-Wing (×3), 2-String Kite (×2), Cell Forcing Chains, Finned Fish, Nice Loops/AICs, W-Wing, XY-Chain, XY-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 (16)
  1. Step 4 · 2-String Kite advanced
    Rules out 8 from R8C9.
  2. Step 5 · ALS-XZ expert
    Rules out 3 from R4C7.
  3. Step 6 · ALS-XZ expert
    Rules out 8 from R4C7.
  4. Step 7 · Nice Loops/AICs expert
    Rules out 1 from R1C8.
  5. Step 9 · Cell Forcing Chains expert
    Rules out 4 from R4C7.
  6. Step 12 · Finned Fish expert
    Rules out 8 from R4C5.
  7. Step 13 · WXYZ-Wing expert
    Rules out 3 from R3C8.
  8. Step 14 · ALS-XZ expert
    Rules out 1 from R2C1.
  9. Step 20 · WXYZ-Wing expert
    Rules out 3 from R5C2, R5C3, R6C8, R6C9.
  10. Step 22 · ALS-XZ expert
    Rules out 4 from R5C3.
  11. Step 24 · 2-String Kite advanced
    Rules out 3 from R6C5.
  12. Step 25 · W-Wing advanced
    Rules out 7 from R4C2, R6C5.
  13. Step 31 · ALS-XZ expert
    Rules out 6 from R7C4.
  14. Step 32 · WXYZ-Wing expert
    Rules out 2 from R7C7.
  15. Step 34 · XY-Wing advanced
    Rules out 1 from R3C2.
  16. Step 35 · XY-Chain expert
    Rules out 3 from R7C8, R9C8.

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.