EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 17: 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 17 of 150 in Extreme Sudoku 1
Difficulty
Expert 5 (expert and beyond), from the opening third of the book
Key technique
Nice Loops/AICs
Hard steps
18 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: Nice Loops/AICs

An alternating chain of strong and weak links. Whichever end is true, the conclusion holds, so the digit at the marked cell is ruled out.

Other advanced and expert techniques in this solve: XY-Chain (×4), ALS-XZ (×3), W-Wing (×2), 2-String Kite, Sue de Coq, WXYZ-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 (18)
  1. Step 6 · WXYZ-Wing expert
    Rules out 7 from R5C3.
  2. Step 8 · Sue de Coq expert
    Rules out 3 from R1C7, R1C8; 1 from R2C1; 6 from R2C1.
  3. Step 9 · ALS-XZ expert
    Rules out 6 from R4C5.
  4. Step 11 · ALS-XZ expert
    Rules out 7 from R4C5.
  5. Step 12 · ALS-XZ expert
    Rules out 8 from R5C6.
  6. Step 13 · Nice Loops/AICs expert
    Rules out 1 from R1C3.
  7. Step 14 · Nice Loops/AICs expert
    Rules out 6 from R2C4.
  8. Step 15 · Nice Loops/AICs expert
    Rules out 6 from R2C7.
  9. Step 16 · Nice Loops/AICs expert
    Rules out 9 from R2C1.
  10. Step 18 · Nice Loops/AICs expert
    Rules out 5 from R2C7, R3C2.
  11. Step 20 · W-Wing advanced
    Rules out 8 from R5C8.
  12. Step 21 · Nice Loops/AICs expert
    Rules out 2 from R5C3.
  13. Step 22 · XY-Chain expert
    Rules out 8 from R5C2, R5C5, R5C7.
  14. Step 28 · 2-String Kite advanced
    Rules out 7 from R7C1.
  15. Step 29 · XY-Chain expert
    Rules out 2 from R1C5, R3C2.
  16. Step 31 · XY-Chain expert
    Rules out 2 from R1C1.
  17. Step 33 · XY-Chain expert
    Rules out 1 from R1C7, R2C3.
  18. Step 39 · W-Wing advanced
    Rules out 6 from R7C7, R7C8, R7C9.

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.