EXTREMEPUZZLE BOOKS

Extreme Sudoku 3, puzzle 137: 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 137 of 150 in Extreme Sudoku 3
Difficulty
Expert 5 (expert and beyond), from the final, hardest third of the book
Key technique
Nice Loops/AICs
Hard steps
16 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 (×4), Finned Fish (×2), ALS-XZ, Cell Forcing Chains, Empty Rectangle, W-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 (16)
  1. Step 6 · Empty Rectangle advanced
    Rules out 8 from R5C4.
  2. Step 7 · Finned Fish expert
    Rules out 6 from R9C4, R9C5.
  3. Step 8 · Nice Loops/AICs expert
    Rules out 7 from R5C8.
  4. Step 9 · Nice Loops/AICs expert
    Rules out 8 from R8C6.
  5. Step 10 · Nice Loops/AICs expert
    Rules out 1 from R8C6.
  6. Step 12 · Cell Forcing Chains expert
    Rules out 1 from R1C7.
  7. Step 15 · ALS-XZ expert
    Rules out 9 from R9C4, R9C6.
  8. Step 16 · Nice Loops/AICs expert
    Rules out 9 from R3C8.
  9. Step 17 · Nice Loops/AICs expert
    Rules out 7 from R4C8, R5C4.
  10. Step 20 · Finned Fish expert
    Rules out 1 from R2C5.
  11. Step 21 · XY-Chain expert
    Rules out 2 from R9C5.
  12. Step 24 · XY-Chain expert
    Rules out 8 from R2C7, R5C5.
  13. Step 30 · W-Wing advanced
    Rules out 6 from R7C5.
  14. Step 31 · XY-Chain expert
    Rules out 6 from R1C4, R1C6.
  15. Step 33 · XY-Wing advanced
    Rules out 1 from R1C4.
  16. Step 37 · XY-Chain expert
    Rules out 3 from R2C1, R6C3.

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.