EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 104: 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 104 of 150 in Extreme Sudoku 1
Difficulty
Expert 5 (expert and beyond), from the final, hardest third of the book
Key technique
ALS-XZ
Hard steps
11 of 36 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: ALS-XZ

Two almost-locked sets (n cells with n+1 candidates) share a restricted digit X. Then a digit Z common to both must be in one of them, so cells seeing all of its copies cannot be Z.

Other advanced and expert techniques in this solve: XY-Chain (×3), Cell Forcing Chains, Finned Fish, W-Wing, 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 (11)
  1. Step 11 · Finned Fish expert
    Rules out 3 from R5C6.
  2. Step 12 · XY-Wing advanced
    Rules out 1 from R5C8.
  3. Step 13 · WXYZ-Wing expert
    Rules out 4 from R9C1.
  4. Step 16 · ALS-XZ expert
    Rules out 9 from R6C8.
  5. Step 18 · Cell Forcing Chains expert
    Rules out 1 from R1C2.
  6. Step 21 · XY-Chain expert
    Rules out 3 from R5C7.
  7. Step 22 · ALS-XZ expert
    Rules out 1 from R6C8.
  8. Step 23 · ALS-XZ expert
    Rules out 7 from R6C9, R7C7.
  9. Step 26 · W-Wing advanced
    Rules out 5 from R4C5, R5C3.
  10. Step 28 · XY-Chain expert
    Rules out 8 from R1C6, R4C4.
  11. Step 31 · XY-Chain expert
    Rules out 1 from R6C9.

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.