EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 76: 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 76 of 150 in Extreme Sudoku 1
Difficulty
Expert 5 (expert and beyond), from the middle third of the book
Key technique
XY-Chain
Hard steps
18 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: Nice Loops/AICs (×3), XY-Wing (×3), ALS-XZ, Cell Forcing Chains, Empty Rectangle, 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 (18)
  1. Step 11 · Cell Forcing Chains expert
    Rules out 4 from R1C1.
  2. Step 13 · Empty Rectangle advanced
    Rules out 4 from R7C3.
  3. Step 14 · XY-Chain expert
    Rules out 8 from R5C4.
  4. Step 16 · WXYZ-Wing expert
    Rules out 3 from R7C1.
  5. Step 17 · XY-Wing advanced
    Rules out 4 from R3C1, R9C3.
  6. Step 18 · ALS-XZ expert
    Rules out 8 from R1C3.
  7. Step 21 · Nice Loops/AICs expert
    Rules out 1 from R2C1.
  8. Step 22 · Nice Loops/AICs expert
    Rules out 4 from R3C8.
  9. Step 23 · Nice Loops/AICs expert
    Rules out 4 from R7C6.
  10. Step 25 · XY-Wing advanced
    Rules out 3 from R8C4.
  11. Step 26 · XY-Chain expert
    Rules out 4 from R8C8.
  12. Step 28 · XY-Chain expert
    Rules out 4 from R3C9.
  13. Step 31 · W-Wing advanced
    Rules out 9 from R4C9, R6C4.
  14. Step 32 · XY-Chain expert
    Rules out 1 from R2C3, R6C2.
  15. Step 36 · XY-Chain expert
    Rules out 9 from R2C6, R4C4.
  16. Step 39 · XY-Wing advanced
    Rules out 4 from R9C1.
  17. Step 40 · XY-Chain expert
    Rules out 6 from R8C1.
  18. Step 43 · XY-Chain expert
    Rules out 5 from R2C3, R9C1.

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.