EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 31: 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 31 of 150 in Extreme Sudoku 3
Difficulty
Expert 7 (expert and beyond), from the opening third of the book
Key technique
Nice Loops/AICs
Hard steps
15 of 37 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), Cell Forcing Chains, Finned Fish, Sue de Coq, W-Wing, WXYZ-Wing, 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 (15)
  1. Step 4 · Finned Fish expert
    Rules out 3 from R4C1, R4C2.
  2. Step 5 · ALS-XZ expert
    Rules out 5 from R8C3.
  3. Step 6 · ALS-XZ expert
    Rules out 2 from R7C3.
  4. Step 9 · WXYZ-Wing expert
    Rules out 4 from R2C1, R3C1.
  5. Step 10 · Nice Loops/AICs expert
    Rules out 4 from R8C3.
  6. Step 16 · W-Wing advanced
    Rules out 4 from R3C2, R4C3.
  7. Step 18 · Sue de Coq expert
    Rules out 5 from R2C4, R2C6, R3C4; 4 from R3C4, R3C5.
  8. Step 19 · Nice Loops/AICs expert
    Rules out 4 from R1C6.
  9. Step 20 · Nice Loops/AICs expert
    Rules out 3 from R7C4.
  10. Step 21 · Nice Loops/AICs expert
    Rules out 3 from R7C5.
  11. Step 22 · Cell Forcing Chains expert
    Rules out 9 from R1C7.
  12. Step 29 · XY-Chain expert
    Rules out 4 from R1C5.
  13. Step 30 · XY-Chain expert
    Rules out 1 from R6C5.
  14. Step 32 · XY-Wing advanced
    Rules out 3 from R7C2.
  15. Step 33 · XY-Chain expert
    Rules out 9 from R1C5, R7C4.

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.