EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 49: 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 49 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
15 of 37 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), 2-String Kite, Empty Rectangle, Finned Fish, Sue de Coq, 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 (15)
  1. Step 5 · X-Wing/Swordfish advanced
    Rules out 5 from R4C1, R4C8, R9C1, R9C8.
  2. Step 6 · 2-String Kite advanced
    Rules out 7 from R6C6.
  3. Step 7 · ALS-XZ expert
    Rules out 8 from R2C5.
  4. Step 8 · ALS-XZ expert
    Rules out 8 from R2C1.
  5. Step 10 · Nice Loops/AICs expert
    Rules out 8 from R1C1.
  6. Step 12 · Nice Loops/AICs expert
    Rules out 5 from R6C3.
  7. Step 17 · Empty Rectangle advanced
    Rules out 6 from R1C1.
  8. Step 19 · Finned Fish expert
    Rules out 1 from R5C4.
  9. Step 20 · Nice Loops/AICs expert
    Rules out 7 from R4C1.
  10. Step 21 · Nice Loops/AICs expert
    Rules out 7 from R6C9.
  11. Step 22 · Nice Loops/AICs expert
    Rules out 7 from R5C6.
  12. Step 23 · WXYZ-Wing expert
    Rules out 1 from R5C9.
  13. Step 28 · ALS-XZ expert
    Rules out 7 from R5C9.
  14. Step 32 · Sue de Coq expert
    Rules out 3 from R6C5; 6 from R7C6, R8C6, R9C6.
  15. Step 33 · XY-Wing advanced
    Rules out 9 from R8C6.

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.