EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 75: 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 75 of 150 in Extreme Sudoku 1
Difficulty
Expert 5 (expert and beyond), from the middle third of the book
Key technique
XY-Chain
Hard steps
20 of 48 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: Nice Loops/AICs (×4), XY-Wing (×3), ALS-XZ (×2), WXYZ-Wing (×2), Finned Fish.

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 (20)
  1. Step 3 · Finned Fish expert
    Rules out 9 from R5C7.
  2. Step 4 · ALS-XZ expert
    Rules out 2 from R1C5.
  3. Step 9 · WXYZ-Wing expert
    Rules out 3 from R5C1, R7C2, R8C2.
  4. Step 11 · ALS-XZ expert
    Rules out 5 from R2C3.
  5. Step 16 · XY-Chain expert
    Rules out 4 from R6C9.
  6. Step 18 · XY-Chain expert
    Rules out 2 from R5C8.
  7. Step 19 · Nice Loops/AICs expert
    Rules out 2 from R5C6.
  8. Step 20 · Nice Loops/AICs expert
    Rules out 8 from R9C8.
  9. Step 21 · XY-Chain expert
    Rules out 7 from R4C8.
  10. Step 22 · WXYZ-Wing expert
    Rules out 7 from R9C7.
  11. Step 23 · Nice Loops/AICs expert
    Rules out 9 from R6C8.
  12. Step 24 · Nice Loops/AICs expert
    Rules out 5 from R6C8.
  13. Step 25 · XY-Wing advanced
    Rules out 3 from R9C8.
  14. Step 28 · XY-Chain expert
    Rules out 5 from R1C4, R2C9.
  15. Step 30 · XY-Chain expert
    Rules out 5 from R1C9, R5C8.
  16. Step 32 · XY-Wing advanced
    Rules out 9 from R5C3.
  17. Step 36 · XY-Chain expert
    Rules out 7 from R4C7.
  18. Step 37 · XY-Chain expert
    Rules out 2 from R4C9.
  19. Step 38 · XY-Chain expert
    Rules out 7 from R4C1, R5C1.
  20. Step 43 · XY-Wing advanced
    Rules out 6 from R7C3.

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.