EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 4: 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 4 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
19 of 44 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: ALS-XZ (×5), WXYZ-Wing (×2), XY-Wing (×2), Finned Fish, Nice Loops/AICs, W-Wing, XYZ-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 (19)
  1. Step 9 · ALS-XZ expert
    Rules out 7 from R8C1.
  2. Step 10 · Nice Loops/AICs expert
    Rules out 4 from R7C8.
  3. Step 11 · ALS-XZ expert
    Rules out 6 from R7C6.
  4. Step 12 · XYZ-Wing advanced
    Rules out 9 from R8C5.
  5. Step 14 · XY-Chain expert
    Rules out 1 from R9C1.
  6. Step 15 · XY-Chain expert
    Rules out 9 from R8C6.
  7. Step 16 · XY-Wing advanced
    Rules out 9 from R7C3.
  8. Step 17 · Finned Fish expert
    Rules out 9 from R5C6.
  9. Step 18 · WXYZ-Wing expert
    Rules out 7 from R9C3.
  10. Step 19 · ALS-XZ expert
    Rules out 1 from R5C8.
  11. Step 21 · ALS-XZ expert
    Rules out 7 from R7C8, R9C1.
  12. Step 22 · WXYZ-Wing expert
    Rules out 6 from R5C8.
  13. Step 23 · ALS-XZ expert
    Rules out 9 from R9C8, R9C9.
  14. Step 27 · XY-Wing advanced
    Rules out 9 from R5C5.
  15. Step 28 · W-Wing advanced
    Rules out 3 from R6C8, R9C7.
  16. Step 30 · XY-Chain expert
    Rules out 6 from R4C7.
  17. Step 34 · XY-Chain expert
    Rules out 9 from R4C1.
  18. Step 36 · XY-Chain expert
    Rules out 6 from R5C4, R9C6.
  19. Step 39 · XY-Chain expert
    Rules out 7 from R7C3.

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.

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More step-by-step solutions: Extreme Sudoku 1 · Extreme Killer Sudoku 1 · Extreme Killer Sudoku 2 · Extreme Sudoku 3 · Extreme Killer Sudoku 3.