EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 61: 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 61 of 150 in Extreme Sudoku 2
Difficulty
Expert 6 (expert and beyond), from the middle third of the book
Key technique
XY-Chain
Hard steps
23 of 47 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: Empty Rectangle (×3), ALS-XZ (×2), Nice Loops/AICs (×2), XYZ-Wing (×2), Cell Forcing Chains, Finned Fish, Skyscraper, W-Wing, WXYZ-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 5 · W-Wing advanced
    Rules out 5 from R1C2, R3C2, R4C1, R5C1.
  2. Step 6 · Finned Fish expert
    Rules out 9 from R7C3.
  3. Step 12 · Empty Rectangle advanced
    Rules out 5 from R6C5.
  4. Step 13 · Empty Rectangle advanced
    Rules out 6 from R6C5.
  5. Step 14 · XY-Chain expert
    Rules out 5 from R2C8.
  6. Step 17 · WXYZ-Wing expert
    Rules out 5 from R6C7.
  7. Step 18 · XYZ-Wing advanced
    Rules out 7 from R5C7.
  8. Step 19 · ALS-XZ expert
    Rules out 7 from R5C5.
  9. Step 20 · Nice Loops/AICs expert
    Rules out 1 from R6C9.
  10. Step 21 · ALS-XZ expert
    Rules out 5 from R6C4.
  11. Step 22 · Nice Loops/AICs expert
    Rules out 2 from R6C4.
  12. Step 23 · Cell Forcing Chains expert
    Rules out 3 from R2C3.
  13. Step 27 · Skyscraper advanced
    Rules out 5 from R5C7.
  14. Step 29 · XY-Wing advanced
    Rules out 7 from R5C4.
  15. Step 32 · Empty Rectangle advanced
    Rules out 1 from R3C3.
  16. Step 33 · XY-Chain expert
    Rules out 1 from R1C7.
  17. Step 35 · XY-Chain expert
    Rules out 5 from R1C8, R7C5.
  18. Step 37 · XY-Chain expert
    Rules out 7 from R3C9, R4C8.
  19. Step 38 · XY-Chain expert
    Rules out 2 from R9C2.
  20. Step 39 · XY-Chain expert
    Rules out 6 from R3C1.
  21. Step 40 · XY-Chain expert
    Rules out 8 from R3C9.
  22. Step 42 · XYZ-Wing advanced
    Rules out 9 from R4C6.
  23. Step 44 · XY-Chain expert
    Rules out 1 from R1C3, R4C1.

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.