EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 98: 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 98 of 150 in Extreme Sudoku 1
Difficulty
Expert 7 (expert and beyond), from the middle third of the book
Key technique
XY-Chain
Hard steps
22 of 40 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), W-Wing (×3), 2-String Kite (×2), Sue de Coq (×2), ALS-XZ, Cell Forcing Chains, Coloring/Multi-coloring, Nice Loops/AICs, Skyscraper, 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 (22)
  1. Step 3 · XY-Wing advanced
    Rules out 5 from R4C1.
  2. Step 5 · WXYZ-Wing expert
    Rules out 3 from R4C7.
  3. Step 6 · Sue de Coq expert
    Rules out 3 from R5C4, R5C5.
  4. Step 7 · 2-String Kite advanced
    Rules out 3 from R8C7.
  5. Step 8 · Coloring/Multi-coloring expert
    Rules out 3 from R7C4, R7C5, R7C6.
  6. Step 9 · ALS-XZ expert
    Rules out 9 from R7C5, R9C5.
  7. Step 10 · Nice Loops/AICs expert
    Rules out 9 from R7C7.
  8. Step 11 · Cell Forcing Chains expert
    Rules out 3 from R4C1.
  9. Step 18 · Skyscraper advanced
    Rules out 4 from R1C9, R2C2.
  10. Step 19 · Sue de Coq expert
    Rules out 5 from R1C2, R2C2; 6 from R1C3; 9 from R3C4.
  11. Step 20 · W-Wing advanced
    Rules out 9 from R1C8, R2C2.
  12. Step 22 · W-Wing advanced
    Rules out 3 from R1C4, R3C9.
  13. Step 24 · 2-String Kite advanced
    Rules out 5 from R7C9.
  14. Step 25 · W-Wing advanced
    Rules out 9 from R9C8.
  15. Step 26 · XY-Chain expert
    Rules out 9 from R8C3.
  16. Step 27 · XY-Wing advanced
    Rules out 9 from R1C4.
  17. Step 28 · XY-Chain expert
    Rules out 5 from R1C8, R1C9.
  18. Step 30 · XY-Chain expert
    Rules out 9 from R1C2, R3C2, R9C3.
  19. Step 31 · XY-Wing advanced
    Rules out 1 from R1C2.
  20. Step 32 · XY-Wing advanced
    Rules out 9 from R9C6.
  21. Step 35 · XY-Chain expert
    Rules out 5 from R2C9.
  22. Step 36 · XY-Chain expert
    Rules out 9 from R7C6.

The book

Classic 9×9 sudoku with the warm-up taken out. Every grid sits at the top of the expert range or beyond it, and the book ramps from hard to brutal.

150 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 Killer Sudoku 1 · Extreme Sudoku 2 · Extreme Killer Sudoku 2 · Extreme Sudoku 3 · Extreme Killer Sudoku 3.