EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 117: 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 117 of 150 in Extreme Sudoku 3
Difficulty
Expert 7 (expert and beyond), from the final, hardest third of the book
Key technique
Nice Loops/AICs
Hard steps
20 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), XY-Chain (×4), W-Wing (×2), Cell Forcing Chains, Finned Fish, Sue de Coq, WXYZ-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 (20)
  1. Step 5 · Finned Fish expert
    Rules out 1 from R7C7.
  2. Step 6 · ALS-XZ expert
    Rules out 2 from R6C1, R9C3.
  3. Step 7 · ALS-XZ expert
    Rules out 2 from R5C5.
  4. Step 8 · Nice Loops/AICs expert
    Rules out 3 from R2C4, R3C1, R3C3.
  5. Step 10 · ALS-XZ expert
    Rules out 8 from R2C2, R9C3.
  6. Step 11 · Nice Loops/AICs expert
    Rules out 5 from R2C7.
  7. Step 12 · Nice Loops/AICs expert
    Rules out 1 from R9C1.
  8. Step 14 · Cell Forcing Chains expert
    Rules out 7 from R1C6, R2C6, R4C5, R6C6 and 3 more; 8 from R1C6, R2C6, R7C5, R8C5 and 5 more; 5 from R1C7, R2C1, R2C6.
  9. Step 16 · W-Wing advanced
    Rules out 7 from R3C7, R3C9.
  10. Step 17 · WXYZ-Wing expert
    Rules out 7 from R2C8.
  11. Step 20 · ALS-XZ expert
    Rules out 2 from R9C1.
  12. Step 21 · Nice Loops/AICs expert
    Rules out 8 from R3C5.
  13. Step 24 · W-Wing advanced
    Rules out 7 from R3C1.
  14. Step 25 · Sue de Coq expert
    Rules out 8 from R2C8.
  15. Step 26 · Nice Loops/AICs expert
    Rules out 3 from R2C1.
  16. Step 27 · XY-Chain expert
    Rules out 9 from R7C1.
  17. Step 31 · XY-Chain expert
    Rules out 3 from R1C1.
  18. Step 33 · X-Wing/Swordfish advanced
    Rules out 7 from R2C3, R4C3.
  19. Step 34 · XY-Chain expert
    Rules out 9 from R4C9.
  20. Step 37 · XY-Chain expert
    Rules out 6 from R1C9, R3C1.

The book

Volume three: 150 new classic 9×9 grids, none repeated from books 1 or 2, 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.

On Amazon from 8 Dec About the book

Try a free sample puzzle (PDF) · prints on A4 or US Letter

More step-by-step solutions: Extreme Sudoku 1 · Extreme Killer Sudoku 1 · Extreme Sudoku 2 · Extreme Killer Sudoku 2 · Extreme Killer Sudoku 3.