EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 138: 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 138 of 150 in Extreme Sudoku 2
Difficulty
Expert 6 (expert and beyond), from the final, hardest third of the book
Key technique
XY-Chain
Hard steps
23 of 49 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: XY-Wing (×4), ALS-XZ (×2), Empty Rectangle (×2), Nice Loops/AICs (×2), WXYZ-Wing (×2), Cell Forcing Chains, Sue de Coq, W-Wing, X-Wing/Swordfish.

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 4 · ALS-XZ expert
    Rules out 8 from R4C6.
  2. Step 5 · Nice Loops/AICs expert
    Rules out 7 from R6C6.
  3. Step 6 · Cell Forcing Chains expert
    Rules out 5 from R3C2.
  4. Step 10 · Empty Rectangle advanced
    Rules out 7 from R5C6.
  5. Step 11 · Nice Loops/AICs expert
    Rules out 3 from R4C2.
  6. Step 13 · XY-Wing advanced
    Rules out 6 from R2C8.
  7. Step 14 · XY-Chain expert
    Rules out 6 from R2C6, R3C1.
  8. Step 19 · X-Wing/Swordfish advanced
    Rules out 9 from R4C6, R7C6.
  9. Step 21 · XY-Chain expert
    Rules out 3 from R7C1.
  10. Step 22 · XY-Wing advanced
    Rules out 3 from R8C6.
  11. Step 23 · XY-Chain expert
    Rules out 7 from R9C5.
  12. Step 24 · XY-Chain expert
    Rules out 7 from R9C6.
  13. Step 25 · WXYZ-Wing expert
    Rules out 7 from R7C9.
  14. Step 26 · WXYZ-Wing expert
    Rules out 6 from R7C9.
  15. Step 27 · Sue de Coq expert
    Rules out 4 from R5C5; 7 from R5C5; 3 from R7C6.
  16. Step 29 · XY-Chain expert
    Rules out 6 from R7C8, R8C6.
  17. Step 31 · ALS-XZ expert
    Rules out 1 from R4C6.
  18. Step 35 · Empty Rectangle advanced
    Rules out 3 from R5C8.
  19. Step 36 · XY-Wing advanced
    Rules out 8 from R6C2.
  20. Step 39 · XY-Wing advanced
    Rules out 6 from R5C7.
  21. Step 40 · W-Wing advanced
    Rules out 8 from R5C9.
  22. Step 42 · XY-Chain expert
    Rules out 2 from R1C6, R2C6, R5C5.
  23. Step 45 · XY-Chain expert
    Rules out 8 from R3C1, R4C2.

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.