EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 131: 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 131 of 150 in Extreme Sudoku 1
Difficulty
Expert 7 (expert and beyond), from the final, hardest third of the book
Key technique
Nice Loops/AICs
Hard steps
18 of 37 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: ALS-XZ (×2), WXYZ-Wing (×2), 2-String Kite, Cell Forcing Chains, Empty Rectangle, Finned Fish, Sue de Coq, Unique Rectangles, W-Wing, XY-Chain.

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 5 · WXYZ-Wing expert
    Rules out 5 from R4C9.
  2. Step 6 · ALS-XZ expert
    Rules out 7 from R5C9.
  3. Step 8 · Finned Fish expert
    Rules out 9 from R2C4.
  4. Step 9 · Nice Loops/AICs expert
    Rules out 5 from R1C8.
  5. Step 10 · W-Wing advanced
    Rules out 3 from R1C5, R2C8.
  6. Step 12 · WXYZ-Wing expert
    Rules out 9 from R9C8.
  7. Step 13 · Nice Loops/AICs expert
    Rules out 9 from R9C7.
  8. Step 14 · Nice Loops/AICs expert
    Rules out 9 from R7C7.
  9. Step 15 · Nice Loops/AICs expert
    Rules out 6 from R7C4.
  10. Step 16 · Cell Forcing Chains expert
    Rules out 9 from R1C9.
  11. Step 20 · ALS-XZ expert
    Rules out 6 from R3C6.
  12. Step 21 · Nice Loops/AICs expert
    Rules out 2 from R9C1.
  13. Step 23 · 2-String Kite advanced
    Rules out 2 from R2C4.
  14. Step 24 · Sue de Coq expert
    Rules out 7 from R3C4; 5 from R6C5.
  15. Step 25 · Empty Rectangle advanced
    Rules out 5 from R9C4.
  16. Step 26 · Nice Loops/AICs expert
    Rules out 4 from R6C3.
  17. Step 30 · XY-Chain expert
    Rules out 5 from R6C4.
  18. Step 35 · Unique Rectangles advanced
    Rules out 4 from R2C5; 7 from R2C5.

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.