EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 115: 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 115 of 150 in Extreme Sudoku 1
Difficulty
Expert 6 (expert and beyond), from the final, hardest third of the book
Key technique
XY-Chain
Hard steps
21 of 47 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), Empty Rectangle (×2), XY-Wing (×2), XYZ-Wing (×2), 2-String Kite, Cell Forcing Chains, Finned Fish, Nice Loops/AICs, 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 (21)
  1. Step 5 · Empty Rectangle advanced
    Rules out 1 from R5C3.
  2. Step 6 · Empty Rectangle advanced
    Rules out 9 from R4C3.
  3. Step 7 · XYZ-Wing advanced
    Rules out 4 from R3C2.
  4. Step 8 · Finned Fish expert
    Rules out 1 from R5C2.
  5. Step 9 · WXYZ-Wing expert
    Rules out 1 from R9C5.
  6. Step 10 · Cell Forcing Chains expert
    Rules out 9 from R2C6.
  7. Step 13 · XYZ-Wing advanced
    Rules out 8 from R7C8.
  8. Step 15 · XY-Chain expert
    Rules out 4 from R9C2.
  9. Step 16 · ALS-XZ expert
    Rules out 3 from R4C1, R5C1, R6C1.
  10. Step 17 · ALS-XZ expert
    Rules out 1 from R6C3.
  11. Step 18 · Nice Loops/AICs expert
    Rules out 9 from R4C5.
  12. Step 19 · W-Wing advanced
    Rules out 8 from R5C6, R9C5.
  13. Step 22 · XY-Chain expert
    Rules out 3 from R1C1.
  14. Step 24 · XY-Chain expert
    Rules out 2 from R5C1, R6C1.
  15. Step 25 · XY-Chain expert
    Rules out 7 from R5C6, R6C6.
  16. Step 27 · XY-Chain expert
    Rules out 2 from R2C8.
  17. Step 28 · 2-String Kite advanced
    Rules out 2 from R4C9.
  18. Step 29 · XY-Chain expert
    Rules out 2 from R8C8.
  19. Step 38 · XY-Wing advanced
    Rules out 4 from R8C2.
  20. Step 39 · XY-Chain expert
    Rules out 3 from R4C2.
  21. Step 42 · XY-Wing advanced
    Rules out 1 from 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.