EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 42: 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 42 of 150 in Extreme Sudoku 2
Difficulty
Expert 7 (expert and beyond), from the opening third of the book
Key technique
XY-Chain
Hard steps
14 of 37 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 (×2), Empty Rectangle (×2), Cell Forcing Chains, Finned Fish, Nice Loops/AICs, Skyscraper, Sue de Coq, W-Wing, WXYZ-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 (14)
  1. Step 5 · Empty Rectangle advanced
    Rules out 3 from R1C1.
  2. Step 7 · Empty Rectangle advanced
    Rules out 3 from R7C6.
  3. Step 8 · Sue de Coq expert
    Rules out 1 from R1C4, R2C4; 2 from R1C4, R5C4, R7C5, R7C6; 6 from R1C4, R2C4.
  4. Step 10 · Cell Forcing Chains expert
    Rules out 9 from R1C4.
  5. Step 14 · ALS-XZ expert
    Rules out 4 from R6C2.
  6. Step 15 · ALS-XZ expert
    Rules out 3 from R8C4.
  7. Step 16 · Skyscraper advanced
    Rules out 3 from R9C2, R9C3.
  8. Step 20 · Nice Loops/AICs expert
    Rules out 6 from R6C8.
  9. Step 22 · Finned Fish expert
    Rules out 6 from R7C9.
  10. Step 23 · WXYZ-Wing expert
    Rules out 8 from R4C6.
  11. Step 24 · XY-Chain expert
    Rules out 4 from R4C9.
  12. Step 27 · XY-Chain expert
    Rules out 6 from R8C9.
  13. Step 31 · XY-Chain expert
    Rules out 1 from R1C6.
  14. Step 33 · W-Wing advanced
    Rules out 7 from R1C7.

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.