EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 101: 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 101 of 150 in Extreme Sudoku 1
Difficulty
Expert 7 (expert and beyond), from the final, hardest third of the book
Key technique
XY-Chain
Hard steps
17 of 46 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), Empty Rectangle (×2), Nice Loops/AICs (×2), 2-String Kite, Cell Forcing Chains, Finned Fish, Sue de Coq, W-Wing, WXYZ-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 9 · Finned Fish expert
    Rules out 5 from R4C8.
  2. Step 11 · WXYZ-Wing expert
    Rules out 7 from R6C8.
  3. Step 12 · ALS-XZ expert
    Rules out 2 from R3C3.
  4. Step 13 · Cell Forcing Chains expert
    Rules out 2 from R1C6.
  5. Step 16 · Sue de Coq expert
    Rules out 2 from R3C9; 7 from R4C8, R5C8; 5 from R5C8, R6C8.
  6. Step 17 · ALS-XZ expert
    Rules out 1 from R7C3, R9C5.
  7. Step 19 · Empty Rectangle advanced
    Rules out 9 from R9C8.
  8. Step 20 · Empty Rectangle advanced
    Rules out 9 from R2C3.
  9. Step 22 · ALS-XZ expert
    Rules out 5 from R3C8.
  10. Step 23 · Nice Loops/AICs expert
    Rules out 2 from R2C1, R2C2, R2C3.
  11. Step 26 · Nice Loops/AICs expert
    Rules out 2 from R3C2.
  12. Step 28 · XY-Chain expert
    Rules out 4 from R8C2.
  13. Step 32 · 2-String Kite advanced
    Rules out 9 from R2C7.
  14. Step 36 · W-Wing advanced
    Rules out 7 from R4C2.
  15. Step 39 · XY-Chain expert
    Rules out 2 from R1C1.
  16. Step 41 · XY-Chain expert
    Rules out 9 from R2C4.
  17. Step 42 · XY-Chain expert
    Rules out 3 from R1C9.

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.