EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 142: 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 142 of 150 in Extreme Sudoku 3
Difficulty
Expert 7 (expert and beyond), from the final, hardest third of the book
Key technique
Nice Loops/AICs
Hard steps
22 of 46 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 (×3), Finned Fish (×3), XY-Chain (×2), 2-String Kite, Cell Forcing Chains, Sue de Coq, W-Wing, WXYZ-Wing, X-Wing/Swordfish, XY-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 (22)
  1. Step 3 · Finned Fish expert
    Rules out 1 from R8C6.
  2. Step 4 · ALS-XZ expert
    Rules out 2 from R4C3.
  3. Step 5 · ALS-XZ expert
    Rules out 3 from R3C3.
  4. Step 6 · Cell Forcing Chains expert
    Rules out 5 from R1C1, R1C2, R2C6; 2 from R1C6, R8C1; 8 from R1C6, R8C1.
  5. Step 8 · 2-String Kite advanced
    Rules out 8 from R7C9.
  6. Step 14 · Finned Fish expert
    Rules out 2 from R8C4, R8C6.
  7. Step 15 · ALS-XZ expert
    Rules out 7 from R4C3.
  8. Step 16 · Nice Loops/AICs expert
    Rules out 8 from R8C5.
  9. Step 17 · Nice Loops/AICs expert
    Rules out 4 from R2C3.
  10. Step 21 · Nice Loops/AICs expert
    Rules out 9 from R7C9.
  11. Step 22 · Sue de Coq expert
    Rules out 8 from R1C8; 6 from R7C7; 7 from R7C7.
  12. Step 23 · Nice Loops/AICs expert
    Rules out 6 from R5C6.
  13. Step 24 · Nice Loops/AICs expert
    Rules out 6 from R5C7.
  14. Step 25 · Nice Loops/AICs expert
    Rules out 7 from R1C7.
  15. Step 26 · Nice Loops/AICs expert
    Rules out 9 from R7C7.
  16. Step 31 · W-Wing advanced
    Rules out 9 from R7C6.
  17. Step 33 · XY-Chain expert
    Rules out 9 from R8C8.
  18. Step 34 · WXYZ-Wing expert
    Rules out 7 from R4C6.
  19. Step 36 · XY-Wing advanced
    Rules out 6 from R4C7.
  20. Step 38 · Finned Fish expert
    Rules out 7 from R8C8.
  21. Step 42 · X-Wing/Swordfish advanced
    Rules out 6 from R7C4, R7C8.
  22. Step 43 · XY-Chain expert
    Rules out 2 from R1C2, R5C1.

The book

Volume three: 150 new classic 9×9 grids, none repeated from books 1 or 2, ramping from hard to brutal.

150 new 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.

On Amazon from 8 Dec About the book

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

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