EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 105: 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 105 of 150 in Extreme Sudoku 2
Difficulty
Expert 6 (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: ALS-XZ (×4), Cell Forcing Chains, Coloring/Multi-coloring, Empty Rectangle, WXYZ-Wing, XY-Chain.

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 · ALS-XZ expert
    Rules out 7 from R8C2.
  2. Step 7 · Nice Loops/AICs expert
    Rules out 9 from R5C7.
  3. Step 8 · Nice Loops/AICs expert
    Rules out 9 from R5C8.
  4. Step 9 · Cell Forcing Chains expert
    Rules out 8 from R5C8.
  5. Step 16 · Empty Rectangle advanced
    Rules out 9 from R4C9.
  6. Step 17 · ALS-XZ expert
    Rules out 9 from R4C2, R4C7.
  7. Step 19 · ALS-XZ expert
    Rules out 6 from R9C1.
  8. Step 20 · Coloring/Multi-coloring expert
    Rules out 6 from R1C2, R3C2.
  9. Step 21 · Nice Loops/AICs expert
    Rules out 6 from R5C1.
  10. Step 23 · XY-Chain expert
    Rules out 7 from R7C2.
  11. Step 26 · WXYZ-Wing expert
    Rules out 2 from R5C2.
  12. Step 27 · Nice Loops/AICs expert
    Rules out 9 from R1C2.
  13. Step 29 · ALS-XZ expert
    Rules out 2 from R4C7.
  14. Step 30 · Nice Loops/AICs expert
    Rules out 1 from R3C7, R4C9.
  15. Step 32 · Nice Loops/AICs expert
    Rules out 9 from R6C9.
  16. Step 34 · Nice Loops/AICs expert
    Rules out 6 from R2C7.

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.

Buy on Amazon US Buy on Amazon UK
Other Amazon stores
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 Killer Sudoku 2 · Extreme Sudoku 3 · Extreme Killer Sudoku 3.