EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 97: 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 97 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
23 of 47 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: XYZ-Wing (×4), Nice Loops/AICs (×3), ALS-XZ (×2), Empty Rectangle (×2), Cell Forcing Chains, Coloring/Multi-coloring, Finned Fish, Skyscraper, Unique Rectangles, W-Wing, WXYZ-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 6 · XYZ-Wing advanced
    Rules out 2 from R4C8.
  2. Step 7 · Unique Rectangles advanced
    Rules out 2 from R3C1; 6 from R3C1.
  3. Step 10 · XYZ-Wing advanced
    Rules out 2 from R4C1.
  4. Step 11 · W-Wing advanced
    Rules out 6 from R4C1.
  5. Step 12 · Finned Fish expert
    Rules out 4 from R4C4, R4C5.
  6. Step 13 · Nice Loops/AICs expert
    Rules out 9 from R9C1.
  7. Step 14 · Nice Loops/AICs expert
    Rules out 1 from R4C7.
  8. Step 15 · Nice Loops/AICs expert
    Rules out 4 from R5C6.
  9. Step 16 · Cell Forcing Chains expert
    Rules out 2 from R1C1.
  10. Step 22 · Empty Rectangle advanced
    Rules out 2 from R7C1.
  11. Step 23 · Empty Rectangle advanced
    Rules out 2 from R5C9.
  12. Step 24 · XYZ-Wing advanced
    Rules out 6 from R5C9.
  13. Step 26 · XY-Chain expert
    Rules out 1 from R6C6.
  14. Step 27 · XY-Chain expert
    Rules out 3 from R7C6.
  15. Step 28 · XYZ-Wing advanced
    Rules out 7 from R8C5.
  16. Step 29 · Skyscraper advanced
    Rules out 7 from R3C4.
  17. Step 30 · WXYZ-Wing expert
    Rules out 2 from R6C5.
  18. Step 31 · Coloring/Multi-coloring expert
    Rules out 2 from R7C9.
  19. Step 32 · ALS-XZ expert
    Rules out 9 from R8C5.
  20. Step 33 · ALS-XZ expert
    Rules out 6 from R5C8.
  21. Step 36 · X-Wing/Swordfish advanced
    Rules out 4 from R7C1.
  22. Step 37 · XY-Chain expert
    Rules out 2 from R7C2.
  23. Step 42 · XY-Chain expert
    Rules out 4 from R6C4.

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.