EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, 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 2
Difficulty
Expert 5 (expert and beyond), from the opening third of the book
Key technique
XY-Chain
Hard steps
23 of 53 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: XY-Chain

A chain of two-candidate cells, each linked to the next. Whichever way the start cell goes, one end of the chain holds the digit, so cells seeing both ends cannot.

Other advanced and expert techniques in this solve: 2-String Kite (×4), Empty Rectangle (×4), ALS-XZ (×2), Coloring/Multi-coloring, Finned Fish, Nice Loops/AICs, Skyscraper, W-Wing, 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 (23)
  1. Step 3 · Skyscraper advanced
    Rules out 4 from R1C1, R7C2.
  2. Step 6 · 2-String Kite advanced
    Rules out 4 from R7C9.
  3. Step 7 · 2-String Kite advanced
    Rules out 4 from R2C9.
  4. Step 8 · Empty Rectangle advanced
    Rules out 4 from R5C2.
  5. Step 9 · Empty Rectangle advanced
    Rules out 4 from R6C9.
  6. Step 10 · Finned Fish expert
    Rules out 3 from R8C1.
  7. Step 13 · 2-String Kite advanced
    Rules out 4 from R4C8.
  8. Step 14 · Empty Rectangle advanced
    Rules out 4 from R2C7.
  9. Step 15 · ALS-XZ expert
    Rules out 6 from R7C2.
  10. Step 17 · Coloring/Multi-coloring expert
    Rules out 4 from R5C9.
  11. Step 18 · ALS-XZ expert
    Rules out 3 from R2C5.
  12. Step 23 · 2-String Kite advanced
    Rules out 7 from R5C4.
  13. Step 24 · Empty Rectangle advanced
    Rules out 7 from R2C5.
  14. Step 26 · XY-Chain expert
    Rules out 1 from R5C8.
  15. Step 27 · Nice Loops/AICs expert
    Rules out 7 from R7C4.
  16. Step 30 · XY-Chain expert
    Rules out 6 from R1C5.
  17. Step 31 · XY-Chain expert
    Rules out 8 from R2C9.
  18. Step 32 · XY-Chain expert
    Rules out 8 from R2C8.
  19. Step 33 · XY-Chain expert
    Rules out 6 from R2C5, R5C6.
  20. Step 36 · XY-Wing advanced
    Rules out 4 from R4C5.
  21. Step 39 · W-Wing advanced
    Rules out 4 from R5C8.
  22. Step 42 · XY-Chain expert
    Rules out 6 from R1C4, R2C2.
  23. Step 49 · XY-Chain expert
    Rules out 9 from R1C7.

The book

Volume two: 150 new classic 9×9 grids, none repeated from book 1, 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.

Buy on Amazon US Buy on Amazon UK
Other Amazon stores
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 Killer Sudoku 2 · Extreme Sudoku 3 · Extreme Killer Sudoku 3.