EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 54: 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 54 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
25 of 50 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 (×7), Empty Rectangle (×3), 2-String Kite (×2), Coloring/Multi-coloring, Finned Fish, WXYZ-Wing, 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 (24 of 25)
  1. Step 3 · ALS-XZ expert
    Rules out 4 from R8C6.
  2. Step 4 · ALS-XZ expert
    Rules out 6 from R8C6.
  3. Step 5 · ALS-XZ expert
    Rules out 4 from R4C5.
  4. Step 6 · ALS-XZ expert
    Rules out 6 from R4C5.
  5. Step 8 · 2-String Kite advanced
    Rules out 9 from R5C3.
  6. Step 9 · ALS-XZ expert
    Rules out 9 from R7C6.
  7. Step 13 · Empty Rectangle advanced
    Rules out 2 from R8C6.
  8. Step 14 · Empty Rectangle advanced
    Rules out 2 from R8C9.
  9. Step 15 · Finned Fish expert
    Rules out 1 from R8C9.
  10. Step 18 · WXYZ-Wing expert
    Rules out 4 from R8C4.
  11. Step 19 · ALS-XZ expert
    Rules out 1 from R1C2.
  12. Step 20 · XY-Chain expert
    Rules out 2 from R1C7.
  13. Step 23 · XY-Wing advanced
    Rules out 1 from R5C8.
  14. Step 24 · XY-Chain expert
    Rules out 1 from R4C1, R4C3.
  15. Step 25 · ALS-XZ expert
    Rules out 2 from R1C4.
  16. Step 29 · Empty Rectangle advanced
    Rules out 4 from R6C3.
  17. Step 30 · XY-Chain expert
    Rules out 2 from R1C1, R1C3.
  18. Step 31 · XY-Chain expert
    Rules out 1 from R1C1, R1C3, R1C5.
  19. Step 32 · XY-Chain expert
    Rules out 6 from R9C4.
  20. Step 38 · 2-String Kite advanced
    Rules out 1 from R4C8.
  21. Step 39 · XY-Chain expert
    Rules out 3 from R5C1.
  22. Step 40 · XY-Chain expert
    Rules out 1 from R5C1, R5C3.
  23. Step 41 · XY-Chain expert
    Rules out 2 from R8C3.
  24. Step 42 · Coloring/Multi-coloring expert
    Rules out 1 from R2C3.

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.