EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 146: 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 146 of 150 in Extreme Sudoku 1
Difficulty
Expert 6 (expert and beyond), from the final, hardest third of the book
Key technique
Nice Loops/AICs
Hard steps
26 of 53 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: ALS-XZ (×8), WXYZ-Wing (×2), XY-Chain (×2), Cell Forcing Chains, Empty Rectangle, Finned Fish, XYZ-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 (24 of 26)
  1. Step 5 · Empty Rectangle advanced
    Rules out 3 from R7C5.
  2. Step 7 · XYZ-Wing advanced
    Rules out 8 from R1C1.
  3. Step 8 · WXYZ-Wing expert
    Rules out 8 from R3C6.
  4. Step 9 · ALS-XZ expert
    Rules out 8 from R3C1, R3C2.
  5. Step 10 · ALS-XZ expert
    Rules out 6 from R9C8.
  6. Step 11 · ALS-XZ expert
    Rules out 8 from R5C4.
  7. Step 14 · ALS-XZ expert
    Rules out 4 from R4C1.
  8. Step 15 · Nice Loops/AICs expert
    Rules out 7 from R2C1.
  9. Step 16 · Finned Fish expert
    Rules out 7 from R3C6.
  10. Step 17 · Nice Loops/AICs expert
    Rules out 3 from R6C7.
  11. Step 18 · Nice Loops/AICs expert
    Rules out 3 from R4C7.
  12. Step 19 · Nice Loops/AICs expert
    Rules out 3 from R6C8.
  13. Step 21 · Cell Forcing Chains expert
    Rules out 4 from R1C1.
  14. Step 23 · Nice Loops/AICs expert
    Rules out 6 from R5C8.
  15. Step 25 · ALS-XZ expert
    Rules out 7 from R4C9.
  16. Step 26 · Nice Loops/AICs expert
    Rules out 1 from R5C1, R5C2.
  17. Step 27 · ALS-XZ expert
    Rules out 3 from R2C2, R5C3.
  18. Step 29 · Nice Loops/AICs expert
    Rules out 7 from R3C8.
  19. Step 30 · Nice Loops/AICs expert
    Rules out 4 from R7C3.
  20. Step 31 · ALS-XZ expert
    Rules out 6 from R7C4.
  21. Step 33 · ALS-XZ expert
    Rules out 4 from R7C2, R9C6.
  22. Step 34 · WXYZ-Wing expert
    Rules out 6 from R7C6.
  23. Step 35 · Nice Loops/AICs expert
    Rules out 4 from R5C3.
  24. Step 37 · Nice Loops/AICs expert
    Rules out 4 from R1C4, R3C2.

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.