EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 133: 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 133 of 150 in Extreme Sudoku 2
Difficulty
Expert 5 (expert and beyond), from the final, hardest third of the book
Key technique
XY-Chain
Hard steps
19 of 42 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), Nice Loops/AICs (×2), Skyscraper (×2), 2-String Kite, Cell Forcing Chains, 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 (19)
  1. Step 6 · Skyscraper advanced
    Rules out 4 from R2C3, R7C2.
  2. Step 7 · 2-String Kite advanced
    Rules out 3 from R7C3.
  3. Step 8 · WXYZ-Wing expert
    Rules out 1 from R3C2.
  4. Step 9 · ALS-XZ expert
    Rules out 1 from R1C2.
  5. Step 11 · Cell Forcing Chains expert
    Rules out 1 from R1C5.
  6. Step 13 · Nice Loops/AICs expert
    Rules out 5 from R8C6.
  7. Step 16 · ALS-XZ expert
    Rules out 7 from R7C3.
  8. Step 17 · Nice Loops/AICs expert
    Rules out 3 from R9C4.
  9. Step 21 · Skyscraper advanced
    Rules out 3 from R5C1, R8C3.
  10. Step 23 · W-Wing advanced
    Rules out 7 from R8C1.
  11. Step 24 · XY-Chain expert
    Rules out 7 from R2C3.
  12. Step 25 · XY-Chain expert
    Rules out 6 from R4C2.
  13. Step 26 · ALS-XZ expert
    Rules out 9 from R4C2.
  14. Step 27 · ALS-XZ expert
    Rules out 6 from R6C3.
  15. Step 29 · XY-Chain expert
    Rules out 6 from R4C3.
  16. Step 33 · X-Wing/Swordfish advanced
    Rules out 7 from R1C9.
  17. Step 34 · XY-Chain expert
    Rules out 3 from R7C4.
  18. Step 36 · XY-Wing advanced
    Rules out 1 from R1C8, R3C6.
  19. Step 39 · XY-Chain expert
    Rules out 7 from R7C2.

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.