EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, 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 1
Difficulty
Expert 6 (expert and beyond), from the final, hardest third of the book
Key technique
Nice Loops/AICs
Hard steps
23 of 53 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 (×5), WXYZ-Wing (×2), XY-Chain (×2), Cell Forcing Chains, Finned Fish.

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 (23)
  1. Step 3 · Finned Fish expert
    Rules out 1 from R7C7, R7C8.
  2. Step 4 · ALS-XZ expert
    Rules out 1 from R9C8.
  3. Step 5 · ALS-XZ expert
    Rules out 1 from R6C7.
  4. Step 6 · ALS-XZ expert
    Rules out 2 from R7C4.
  5. Step 8 · WXYZ-Wing expert
    Rules out 7 from R7C6.
  6. Step 9 · Nice Loops/AICs expert
    Rules out 7 from R6C8.
  7. Step 11 · Nice Loops/AICs expert
    Rules out 6 from R1C8.
  8. Step 12 · ALS-XZ expert
    Rules out 6 from R3C2.
  9. Step 13 · Nice Loops/AICs expert
    Rules out 2 from R1C4.
  10. Step 14 · Nice Loops/AICs expert
    Rules out 7 from R4C4.
  11. Step 15 · Nice Loops/AICs expert
    Rules out 2 from R2C7.
  12. Step 17 · Nice Loops/AICs expert
    Rules out 3 from R3C2.
  13. Step 18 · Cell Forcing Chains expert
    Rules out 3 from R1C8.
  14. Step 21 · Nice Loops/AICs expert
    Rules out 6 from R3C4.
  15. Step 22 · ALS-XZ expert
    Rules out 8 from R3C7.
  16. Step 25 · WXYZ-Wing expert
    Rules out 1 from R8C8.
  17. Step 30 · Nice Loops/AICs expert
    Rules out 3 from R1C5, R3C5, R7C6.
  18. Step 31 · Nice Loops/AICs expert
    Rules out 3 from R1C4.
  19. Step 32 · Nice Loops/AICs expert
    Rules out 5 from R7C4.
  20. Step 37 · Nice Loops/AICs expert
    Rules out 3 from R1C9.
  21. Step 38 · Nice Loops/AICs expert
    Rules out 2 from R9C9.
  22. Step 39 · XY-Chain expert
    Rules out 5 from R7C8, R9C6.
  23. Step 48 · XY-Chain expert
    Rules out 6 from R1C1, R1C2, R1C3.

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.

Buy on Amazon US Buy on Amazon UK
Other Amazon stores
About the book

Try a free sample puzzle (PDF) · prints on A4 or US Letter

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