EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 37: 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 37 of 150 in Extreme Sudoku 1
Difficulty
Expert 6 (expert and beyond), from the opening third of the book
Key technique
Nice Loops/AICs
Hard steps
19 of 40 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: Nice Loops/AICs

An alternating chain of strong and weak links. Whichever end is true, the conclusion holds, so the digit at the marked cell is ruled out.

Other advanced and expert techniques in this solve: XY-Chain (×3), ALS-XZ (×2), WXYZ-Wing (×2), XY-Wing (×2), 2-String Kite, Cell Forcing Chains, Finned Fish, W-Wing, X-Wing/Swordfish.

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 (19)
  1. Step 7 · X-Wing/Swordfish advanced
    Rules out 2 from R3C1, R3C4, R3C7, R4C4 and 1 more.
  2. Step 8 · Finned Fish expert
    Rules out 2 from R1C1.
  3. Step 9 · WXYZ-Wing expert
    Rules out 5 from R5C6.
  4. Step 10 · ALS-XZ expert
    Rules out 3 from R3C6.
  5. Step 12 · WXYZ-Wing expert
    Rules out 4 from R3C4.
  6. Step 13 · ALS-XZ expert
    Rules out 5 from R8C7.
  7. Step 14 · Nice Loops/AICs expert
    Rules out 7 from R3C6.
  8. Step 17 · Nice Loops/AICs expert
    Rules out 2 from R1C9.
  9. Step 18 · Nice Loops/AICs expert
    Rules out 7 from R1C9.
  10. Step 19 · Nice Loops/AICs expert
    Rules out 1 from R7C3.
  11. Step 20 · Nice Loops/AICs expert
    Rules out 5 from R9C2.
  12. Step 21 · XY-Wing advanced
    Rules out 9 from R7C2.
  13. Step 23 · XY-Chain expert
    Rules out 9 from R8C2, R9C9.
  14. Step 25 · Cell Forcing Chains expert
    Rules out 7 from R1C4.
  15. Step 31 · XY-Wing advanced
    Rules out 1 from R8C3.
  16. Step 32 · XY-Chain expert
    Rules out 5 from R7C1, R9C1.
  17. Step 34 · W-Wing advanced
    Rules out 7 from R7C7.
  18. Step 35 · 2-String Kite advanced
    Rules out 7 from R8C2.
  19. Step 37 · XY-Chain expert
    Rules out 1 from R7C1.

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.