EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 23: 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 23 of 150 in Extreme Sudoku 3
Difficulty
Expert 6 (expert and beyond), from the opening third of the book
Key technique
Nice Loops/AICs
Hard steps
24 of 38 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), Finned Fish (×3), 2-String Kite (×2), XY-Chain (×2), XY-Wing (×2), Cell Forcing Chains, Coloring/Multi-coloring, Empty Rectangle, W-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 (24)
  1. Step 4 · 2-String Kite advanced
    Rules out 4 from R3C6.
  2. Step 5 · 2-String Kite advanced
    Rules out 5 from R4C7.
  3. Step 6 · Empty Rectangle advanced
    Rules out 8 from R4C6.
  4. Step 7 · W-Wing advanced
    Rules out 7 from R1C4.
  5. Step 8 · Finned Fish expert
    Rules out 3 from R1C7, R3C7.
  6. Step 9 · Finned Fish expert
    Rules out 3 from R9C6.
  7. Step 10 · Finned Fish expert
    Rules out 8 from R5C6.
  8. Step 11 · ALS-XZ expert
    Rules out 3 from R2C6.
  9. Step 13 · ALS-XZ expert
    Rules out 5 from R5C7.
  10. Step 16 · Nice Loops/AICs expert
    Rules out 7 from R1C7.
  11. Step 17 · ALS-XZ expert
    Rules out 5 from R3C9, R6C7.
  12. Step 18 · XY-Chain expert
    Rules out 5 from R4C6.
  13. Step 19 · ALS-XZ expert
    Rules out 9 from R3C6.
  14. Step 20 · Nice Loops/AICs expert
    Rules out 9 from R4C6.
  15. Step 21 · XY-Wing advanced
    Rules out 3 from R1C6, R3C6.
  16. Step 23 · Nice Loops/AICs expert
    Rules out 8 from R8C2.
  17. Step 25 · Nice Loops/AICs expert
    Rules out 4 from R6C5.
  18. Step 26 · Nice Loops/AICs expert
    Rules out 7 from R6C5.
  19. Step 27 · Nice Loops/AICs expert
    Rules out 6 from R3C6.
  20. Step 28 · Nice Loops/AICs expert
    Rules out 4 from R3C4.
  21. Step 29 · Cell Forcing Chains expert
    Rules out 5 from R1C3, R3C7; 1 from R1C6, R3C1, R3C3, R9C3; 9 from R1C7.
  22. Step 31 · Coloring/Multi-coloring expert
    Rules out 4 from R9C6.
  23. Step 32 · XY-Wing advanced
    Rules out 7 from R6C6.
  24. Step 33 · XY-Chain expert
    Rules out 7 from R1C6.

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.