EXTREMEPUZZLE BOOKS

Extreme Sudoku 2, puzzle 51: 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 51 of 150 in Extreme Sudoku 2
Difficulty
Expert 5 (expert and beyond), from the middle third of the book
Key technique
Nice Loops/AICs
Hard steps
13 of 33 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, ALS-XZ, Cell Forcing Chains, Skyscraper, WXYZ-Wing, XY-Wing, XYZ-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 (13)
  1. Step 5 · WXYZ-Wing expert
    Rules out 3 from R8C7.
  2. Step 7 · XYZ-Wing advanced
    Rules out 2 from R9C9.
  3. Step 9 · Nice Loops/AICs expert
    Rules out 2 from R1C4.
  4. Step 10 · Nice Loops/AICs expert
    Rules out 3 from R2C4.
  5. Step 11 · Nice Loops/AICs expert
    Rules out 3 from R2C8.
  6. Step 12 · Cell Forcing Chains expert
    Rules out 7 from R3C9.
  7. Step 14 · Skyscraper advanced
    Rules out 7 from R1C2, R9C1.
  8. Step 19 · ALS-XZ expert
    Rules out 3 from R1C4, R5C5, R6C5.
  9. Step 21 · 2-String Kite advanced
    Rules out 6 from R1C2.
  10. Step 23 · XY-Wing advanced
    Rules out 2 from R1C5, R2C3.
  11. Step 24 · XY-Chain expert
    Rules out 6 from R1C1, R2C1, R2C3, R3C1 and 1 more.
  12. Step 26 · XY-Chain expert
    Rules out 6 from R1C5.
  13. Step 28 · XY-Chain expert
    Rules out 7 from R3C1.

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.

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