EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 21: 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 21 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
17 of 39 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: XY-Chain (×5), ALS-XZ (×2), Finned Fish (×2), 2-String Kite, Empty Rectangle, WXYZ-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 (17)
  1. Step 5 · Finned Fish expert
    Rules out 2 from R3C8.
  2. Step 6 · Nice Loops/AICs expert
    Rules out 9 from R4C9.
  3. Step 7 · Nice Loops/AICs expert
    Rules out 9 from R4C7.
  4. Step 8 · Nice Loops/AICs expert
    Rules out 2 from R2C5.
  5. Step 9 · Nice Loops/AICs expert
    Rules out 1 from R8C6.
  6. Step 12 · WXYZ-Wing expert
    Rules out 4 from R1C5, R2C5.
  7. Step 13 · ALS-XZ expert
    Rules out 8 from R3C8.
  8. Step 14 · ALS-XZ expert
    Rules out 3 from R2C9.
  9. Step 15 · Nice Loops/AICs expert
    Rules out 2 from R2C6.
  10. Step 18 · 2-String Kite advanced
    Rules out 3 from R4C9.
  11. Step 19 · Finned Fish expert
    Rules out 3 from R5C9.
  12. Step 25 · Empty Rectangle advanced
    Rules out 4 from R2C7.
  13. Step 26 · XY-Chain expert
    Rules out 3 from R2C7.
  14. Step 29 · XY-Chain expert
    Rules out 9 from R1C9.
  15. Step 30 · XY-Chain expert
    Rules out 8 from R1C8.
  16. Step 31 · XY-Chain expert
    Rules out 7 from R1C9.
  17. Step 34 · XY-Chain expert
    Rules out 4 from R1C7, R3C3.

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.