EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 67: 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 67 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 45 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 (×4), Nice Loops/AICs (×4), 2-String Kite (×3), Cell Forcing Chains, Finned Fish, 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 (20)
  1. Step 5 · X-Wing/Swordfish advanced
    Rules out 6 from R6C1, R7C1, R7C4, R8C1.
  2. Step 6 · 2-String Kite advanced
    Rules out 7 from R7C2.
  3. Step 7 · Finned Fish expert
    Rules out 7 from R7C3.
  4. Step 8 · Nice Loops/AICs expert
    Rules out 9 from R4C6.
  5. Step 9 · Nice Loops/AICs expert
    Rules out 6 from R7C5.
  6. Step 10 · 2-String Kite advanced
    Rules out 6 from R6C7.
  7. Step 11 · ALS-XZ expert
    Rules out 8 from R7C2, R7C3.
  8. Step 12 · ALS-XZ expert
    Rules out 6 from R8C8.
  9. Step 13 · Nice Loops/AICs expert
    Rules out 8 from R8C1.
  10. Step 14 · Cell Forcing Chains expert
    Rules out 1 from R1C7.
  11. Step 16 · ALS-XZ expert
    Rules out 9 from R4C9.
  12. Step 17 · ALS-XZ expert
    Rules out 1 from R2C2.
  13. Step 18 · Nice Loops/AICs expert
    Rules out 7 from R4C2.
  14. Step 22 · 2-String Kite advanced
    Rules out 9 from R6C7.
  15. Step 23 · XY-Chain expert
    Rules out 2 from R2C5, R6C6.
  16. Step 26 · XY-Chain expert
    Rules out 7 from R3C3.
  17. Step 28 · XY-Chain expert
    Rules out 8 from R6C1.
  18. Step 32 · XY-Chain expert
    Rules out 1 from R1C6.
  19. Step 35 · XY-Chain expert
    Rules out 7 from R2C8, R3C2.
  20. Step 39 · XY-Chain expert
    Rules out 1 from R3C6, R7C4.

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.