EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 139: 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 139 of 150 in Extreme Sudoku 1
Difficulty
Expert 6 (expert and beyond), from the final, hardest third of the book
Key technique
Nice Loops/AICs
Hard steps
18 of 41 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), Cell Forcing Chains, Finned Fish, 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 (18)
  1. Step 4 · Finned Fish expert
    Rules out 1 from R1C5.
  2. Step 5 · Nice Loops/AICs expert
    Rules out 6 from R4C8, R5C8.
  3. Step 6 · Nice Loops/AICs expert
    Rules out 1 from R5C4.
  4. Step 7 · Nice Loops/AICs expert
    Rules out 7 from R8C3.
  5. Step 8 · Cell Forcing Chains expert
    Rules out 1 from R1C3.
  6. Step 13 · ALS-XZ expert
    Rules out 1 from R2C3.
  7. Step 16 · XYZ-Wing advanced
    Rules out 6 from R5C7.
  8. Step 19 · ALS-XZ expert
    Rules out 5 from R1C4.
  9. Step 20 · ALS-XZ expert
    Rules out 2 from R4C8.
  10. Step 21 · XY-Wing advanced
    Rules out 1 from R4C1.
  11. Step 25 · XY-Chain expert
    Rules out 5 from R7C4, R8C4.
  12. Step 26 · WXYZ-Wing expert
    Rules out 5 from R2C4.
  13. Step 29 · Nice Loops/AICs expert
    Rules out 9 from R8C2.
  14. Step 32 · W-Wing advanced
    Rules out 7 from R5C5.
  15. Step 33 · W-Wing advanced
    Rules out 9 from R9C8.
  16. Step 34 · XY-Chain expert
    Rules out 9 from R2C7.
  17. Step 35 · XY-Chain expert
    Rules out 7 from R6C5.
  18. Step 37 · XY-Chain expert
    Rules out 5 from R7C1.

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.