EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 106: 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 106 of 150 in Extreme Sudoku 1
Difficulty
Expert 5 (expert and beyond), from the final, hardest third of the book
Key technique
XY-Chain
Hard steps
15 of 35 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 (×3), W-Wing (×2), 2-String Kite, Cell Forcing Chains, Empty Rectangle, Nice Loops/AICs, 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 (15)
  1. Step 3 · Empty Rectangle advanced
    Rules out 2 from R1C2.
  2. Step 4 · WXYZ-Wing expert
    Rules out 3 from R7C7.
  3. Step 5 · ALS-XZ expert
    Rules out 3 from R9C3.
  4. Step 6 · Cell Forcing Chains expert
    Rules out 3 from R1C7, R1C8, R1C9, R3C3 and 3 more; 8 from R1C9, R6C5; 4 from R4C5, R4C8, R5C5, R6C8 and 1 more.
  5. Step 9 · Nice Loops/AICs expert
    Rules out 2 from R7C3, R9C3.
  6. Step 10 · XY-Wing advanced
    Rules out 6 from R2C3, R9C1.
  7. Step 11 · ALS-XZ expert
    Rules out 2 from R2C1.
  8. Step 13 · W-Wing advanced
    Rules out 2 from R1C6.
  9. Step 14 · ALS-XZ expert
    Rules out 8 from R4C3, R5C3, R7C1.
  10. Step 18 · 2-String Kite advanced
    Rules out 2 from R9C2.
  11. Step 19 · W-Wing advanced
    Rules out 2 from R9C9.
  12. Step 20 · XY-Chain expert
    Rules out 2 from R6C2.
  13. Step 22 · XY-Chain expert
    Rules out 5 from R3C1.
  14. Step 25 · XY-Chain expert
    Rules out 6 from R4C7, R5C7, R7C8.
  15. Step 29 · XY-Chain expert
    Rules out 5 from R3C3, R5C2.

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.