EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 113: 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 113 of 150 in Extreme Sudoku 1
Difficulty
Expert 5 (expert and beyond), from the final, hardest third of the book
Key technique
Nice Loops/AICs
Hard steps
15 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: XY-Chain (×3), 2-String Kite (×2), Finned Fish (×2), ALS-XZ, 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 6 · 2-String Kite advanced
    Rules out 4 from R4C3.
  2. Step 9 · Finned Fish expert
    Rules out 6 from R9C7.
  3. Step 12 · WXYZ-Wing expert
    Rules out 1 from R8C5.
  4. Step 13 · 2-String Kite advanced
    Rules out 1 from R5C8.
  5. Step 14 · ALS-XZ expert
    Rules out 2 from R8C6.
  6. Step 15 · Nice Loops/AICs expert
    Rules out 6 from R1C9, R2C6.
  7. Step 18 · Nice Loops/AICs expert
    Rules out 7 from R4C1.
  8. Step 21 · Nice Loops/AICs expert
    Rules out 2 from R2C1, R3C1.
  9. Step 22 · Nice Loops/AICs expert
    Rules out 4 from R5C5.
  10. Step 24 · Nice Loops/AICs expert
    Rules out 4 from R5C6.
  11. Step 26 · Finned Fish expert
    Rules out 2 from R4C1.
  12. Step 27 · XY-Chain expert
    Rules out 7 from R9C6.
  13. Step 30 · XY-Chain expert
    Rules out 3 from R2C6, R3C6, R8C5.
  14. Step 34 · XY-Wing advanced
    Rules out 1 from R4C9.
  15. Step 36 · XY-Chain expert
    Rules out 6 from R5C7, R6C7.

The book

Classic 9×9 sudoku with the warm-up taken out. Every grid sits at the top of the expert range or beyond it, and the book ramps from hard to brutal.

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