EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 1: 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 1 of 150 in Extreme Sudoku 1
Difficulty
Expert 5 (expert and beyond), from the opening third of the book
Key technique
XY-Chain
Hard steps
17 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: ALS-XZ (×2), Nice Loops/AICs (×2), W-Wing (×2), WXYZ-Wing (×2), 2-String Kite, Finned Fish, Skyscraper, 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 (17)
  1. Step 7 · Skyscraper advanced
    Rules out 7 from R6C5, R8C6.
  2. Step 9 · 2-String Kite advanced
    Rules out 8 from R8C2.
  3. Step 11 · W-Wing advanced
    Rules out 9 from R4C7.
  4. Step 12 · W-Wing advanced
    Rules out 9 from R1C2.
  5. Step 13 · Finned Fish expert
    Rules out 8 from R2C2.
  6. Step 14 · WXYZ-Wing expert
    Rules out 9 from R1C3.
  7. Step 15 · WXYZ-Wing expert
    Rules out 9 from R2C3.
  8. Step 16 · ALS-XZ expert
    Rules out 9 from R6C2.
  9. Step 17 · Nice Loops/AICs expert
    Rules out 3 from R1C4.
  10. Step 18 · Nice Loops/AICs expert
    Rules out 9 from R3C7, R3C8.
  11. Step 21 · XY-Wing advanced
    Rules out 6 from R9C4.
  12. Step 22 · ALS-XZ expert
    Rules out 1 from R5C7.
  13. Step 26 · XY-Chain expert
    Rules out 6 from R1C6, R6C4.
  14. Step 28 · XY-Chain expert
    Rules out 7 from R2C6, R6C6.
  15. Step 29 · XY-Chain expert
    Rules out 9 from R4C8.
  16. Step 34 · XY-Chain expert
    Rules out 8 from R9C2.
  17. Step 37 · XY-Chain expert
    Rules out 8 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.