EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 117: 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 117 of 150 in Extreme Sudoku 2
Difficulty
Expert 7 (expert and beyond), from the final, hardest third of the book
Key technique
XY-Chain
Hard steps
22 of 41 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 (×4), 2-String Kite (×3), Finned Fish (×2), Nice Loops/AICs (×2), Cell Forcing Chains, Sue de Coq, W-Wing, WXYZ-Wing, X-Wing/Swordfish, 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 (22)
  1. Step 4 · 2-String Kite advanced
    Rules out 1 from R6C8.
  2. Step 5 · 2-String Kite advanced
    Rules out 5 from R3C5.
  3. Step 6 · 2-String Kite advanced
    Rules out 7 from R6C3.
  4. Step 7 · XY-Wing advanced
    Rules out 3 from R5C9.
  5. Step 8 · Finned Fish expert
    Rules out 1 from R4C8.
  6. Step 11 · WXYZ-Wing expert
    Rules out 7 from R5C8.
  7. Step 12 · ALS-XZ expert
    Rules out 7 from R6C1.
  8. Step 13 · ALS-XZ expert
    Rules out 9 from R6C1.
  9. Step 14 · Nice Loops/AICs expert
    Rules out 3 from R5C8.
  10. Step 15 · Nice Loops/AICs expert
    Rules out 2 from R9C8.
  11. Step 16 · Cell Forcing Chains expert
    Rules out 4 from R1C2.
  12. Step 22 · ALS-XZ expert
    Rules out 4 from R2C9, R3C9.
  13. Step 23 · ALS-XZ expert
    Rules out 3 from R1C5, R1C8, R3C8, R3C9.
  14. Step 25 · W-Wing advanced
    Rules out 9 from R1C5, R2C5, R6C4.
  15. Step 27 · Finned Fish expert
    Rules out 8 from R2C7, R2C8.
  16. Step 28 · XY-Chain expert
    Rules out 1 from R6C6.
  17. Step 29 · XY-Chain expert
    Rules out 5 from R1C5, R6C5, R9C5.
  18. Step 30 · X-Wing/Swordfish advanced
    Rules out 5 from R2C8.
  19. Step 31 · XY-Chain expert
    Rules out 7 from R4C7.
  20. Step 32 · XY-Chain expert
    Rules out 9 from R5C1.
  21. Step 33 · Sue de Coq expert
    Rules out 9 from R4C7.
  22. Step 36 · XY-Chain expert
    Rules out 4 from R1C7, R1C9, R2C5.

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.