EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 46: 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 46 of 150 in Extreme Sudoku 3
Difficulty
Expert 5 (expert and beyond), from the opening third of the book
Key technique
Nice Loops/AICs
Hard steps
21 of 43 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 (×4), XY-Chain (×4), W-Wing (×3), Cell Forcing Chains, Empty Rectangle, 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 (21)
  1. Step 4 · Finned Fish expert
    Rules out 3 from R8C7.
  2. Step 6 · ALS-XZ expert
    Rules out 2 from R6C9.
  3. Step 7 · Nice Loops/AICs expert
    Rules out 2 from R5C7.
  4. Step 8 · Nice Loops/AICs expert
    Rules out 7 from R9C7.
  5. Step 9 · Nice Loops/AICs expert
    Rules out 7 from R6C7.
  6. Step 10 · Nice Loops/AICs expert
    Rules out 7 from R6C1.
  7. Step 11 · Cell Forcing Chains expert
    Rules out 7 from R1C6.
  8. Step 14 · XY-Chain expert
    Rules out 9 from R9C1.
  9. Step 15 · ALS-XZ expert
    Rules out 1 from R8C3.
  10. Step 17 · ALS-XZ expert
    Rules out 8 from R7C4, R7C6.
  11. Step 18 · ALS-XZ expert
    Rules out 8 from R8C8.
  12. Step 19 · Nice Loops/AICs expert
    Rules out 2 from R6C4.
  13. Step 20 · XY-Chain expert
    Rules out 4 from R3C6, R7C4.
  14. Step 25 · Empty Rectangle advanced
    Rules out 5 from R8C3.
  15. Step 27 · XY-Chain expert
    Rules out 8 from R9C7, R9C9.
  16. Step 28 · Nice Loops/AICs expert
    Rules out 2 from R5C4.
  17. Step 30 · Nice Loops/AICs expert
    Rules out 8 from R5C4.
  18. Step 35 · W-Wing advanced
    Rules out 5 from R5C9.
  19. Step 36 · W-Wing advanced
    Rules out 1 from R9C9.
  20. Step 38 · XY-Chain expert
    Rules out 5 from R4C7.
  21. Step 39 · W-Wing advanced
    Rules out 2 from R4C1.

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.