EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 121: 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 121 of 150 in Extreme Sudoku 3
Difficulty
Expert 5 (expert and beyond), from the final, hardest third of the book
Key technique
Nice Loops/AICs
Hard steps
22 of 49 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), 2-String Kite (×2), WXYZ-Wing (×2), XY-Wing (×2), Cell Forcing Chains, W-Wing, XY-Chain, 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 (22)
  1. Step 5 · WXYZ-Wing expert
    Rules out 1 from R9C4.
  2. Step 6 · Nice Loops/AICs expert
    Rules out 1 from R1C8.
  3. Step 7 · Nice Loops/AICs expert
    Rules out 1 from R5C3.
  4. Step 8 · Cell Forcing Chains expert
    Rules out 6 from R1C2.
  5. Step 11 · 2-String Kite advanced
    Rules out 2 from R4C3.
  6. Step 13 · ALS-XZ expert
    Rules out 9 from R3C3.
  7. Step 14 · ALS-XZ expert
    Rules out 4 from R7C7.
  8. Step 15 · ALS-XZ expert
    Rules out 5 from R4C8.
  9. Step 16 · ALS-XZ expert
    Rules out 1 from R4C8.
  10. Step 17 · Nice Loops/AICs expert
    Rules out 5 from R5C7.
  11. Step 18 · Nice Loops/AICs expert
    Rules out 1 from R5C4.
  12. Step 19 · Nice Loops/AICs expert
    Rules out 2 from R3C1.
  13. Step 22 · Nice Loops/AICs expert
    Rules out 2 from R1C5, R3C3.
  14. Step 24 · Nice Loops/AICs expert
    Rules out 2 from R3C5, R4C6.
  15. Step 26 · W-Wing advanced
    Rules out 6 from R4C5, R5C5, R9C4.
  16. Step 28 · ALS-XZ expert
    Rules out 1 from R4C9.
  17. Step 29 · 2-String Kite advanced
    Rules out 1 from R7C7.
  18. Step 30 · XYZ-Wing advanced
    Rules out 5 from R9C8, R9C9.
  19. Step 31 · XY-Wing advanced
    Rules out 5 from R4C6.
  20. Step 33 · WXYZ-Wing expert
    Rules out 5 from R4C7, R7C9.
  21. Step 39 · XY-Chain expert
    Rules out 4 from R3C5.
  22. Step 42 · XY-Wing advanced
    Rules out 5 from R7C6, R9C7.

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.