EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 103: 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 103 of 150 in Extreme Sudoku 1
Difficulty
Expert 8 (expert and beyond), from the final, hardest third of the book
Key technique
ALS-XZ
Hard steps
20 of 43 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 (×3), WXYZ-Wing (×3), W-Wing (×2), XY-Chain (×2), 2-String Kite, Cell Forcing Chains, Coloring/Multi-coloring, Empty Rectangle, Finned Fish, Sue de Coq.

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 (20)
  1. Step 10 · 2-String Kite advanced
    Rules out 7 from R8C4.
  2. Step 11 · W-Wing advanced
    Rules out 3 from R7C5.
  3. Step 12 · Finned Fish expert
    Rules out 8 from R8C3, R9C3.
  4. Step 13 · WXYZ-Wing expert
    Rules out 8 from R8C5, R9C5.
  5. Step 14 · Coloring/Multi-coloring expert
    Rules out 7 from R8C6.
  6. Step 15 · Empty Rectangle advanced
    Rules out 7 from R9C2.
  7. Step 17 · ALS-XZ expert
    Rules out 4 from R8C7, R9C7.
  8. Step 18 · Nice Loops/AICs expert
    Rules out 8 from R3C6.
  9. Step 21 · W-Wing advanced
    Rules out 3 from R1C5.
  10. Step 22 · WXYZ-Wing expert
    Rules out 3 from R9C7.
  11. Step 23 · Sue de Coq expert
    Rules out 3 from R8C4.
  12. Step 24 · ALS-XZ expert
    Rules out 3 from R9C5.
  13. Step 25 · Nice Loops/AICs expert
    Rules out 3 from R3C9.
  14. Step 26 · Nice Loops/AICs expert
    Rules out 3 from R8C9.
  15. Step 27 · Cell Forcing Chains expert
    Rules out 9 from R1C4, R8C3, R9C5; 5 from R3C9; 1 from R9C3.
  16. Step 29 · ALS-XZ expert
    Rules out 7 from R8C8.
  17. Step 31 · XY-Chain expert
    Rules out 7 from R8C5.
  18. Step 33 · WXYZ-Wing expert
    Rules out 2 from R3C8.
  19. Step 34 · ALS-XZ expert
    Rules out 7 from R7C3.
  20. Step 39 · XY-Chain expert
    Rules out 3 from R9C1.

The book

Classic 9×9 sudoku with the warm-up taken out. Every grid sits at the top of the expert range or beyond it, and the book ramps from hard to brutal.

150 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.

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More step-by-step solutions: Extreme Killer Sudoku 1 · Extreme Sudoku 2 · Extreme Killer Sudoku 2 · Extreme Sudoku 3 · Extreme Killer Sudoku 3.