EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, 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 2
Difficulty
Expert 7 (expert and beyond), from the final, hardest third of the book
Key technique
Nice Loops/AICs
Hard steps
18 of 41 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 (×4), WXYZ-Wing (×2), Cell Forcing Chains, Finned Fish, Sue de Coq, X-Wing/Swordfish, XY-Chain, XY-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 4 · Sue de Coq expert
    Rules out 2 from R7C3; 4 from R7C3, R8C4, R9C3; 9 from R9C1, R9C2.
  2. Step 7 · ALS-XZ expert
    Rules out 2 from R7C5.
  3. Step 9 · Nice Loops/AICs expert
    Rules out 5 from R4C1.
  4. Step 10 · Nice Loops/AICs expert
    Rules out 9 from R4C2.
  5. Step 11 · Nice Loops/AICs expert
    Rules out 6 from R1C5.
  6. Step 12 · Nice Loops/AICs expert
    Rules out 6 from R4C3, R4C8.
  7. Step 13 · Cell Forcing Chains expert
    Rules out 6 from R1C4.
  8. Step 18 · XY-Wing advanced
    Rules out 8 from R3C5, R4C6, R6C6.
  9. Step 20 · Finned Fish expert
    Rules out 3 from R3C5.
  10. Step 22 · XY-Chain expert
    Rules out 9 from R9C5.
  11. Step 23 · ALS-XZ expert
    Rules out 7 from R4C1.
  12. Step 24 · ALS-XZ expert
    Rules out 1 from R5C3.
  13. Step 25 · Nice Loops/AICs expert
    Rules out 7 from R4C7.
  14. Step 26 · WXYZ-Wing expert
    Rules out 9 from R6C7.
  15. Step 27 · Nice Loops/AICs expert
    Rules out 8 from R6C4.
  16. Step 29 · ALS-XZ expert
    Rules out 1 from R6C1.
  17. Step 31 · WXYZ-Wing expert
    Rules out 9 from R5C2.
  18. Step 36 · X-Wing/Swordfish advanced
    Rules out 3 from R5C3, R9C3, R9C5.

The book

Volume two: 150 new classic 9×9 grids, none repeated from book 1, ramping from hard to brutal.

150 new 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 Sudoku 1 · Extreme Killer Sudoku 1 · Extreme Killer Sudoku 2 · Extreme Sudoku 3 · Extreme Killer Sudoku 3.