EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 121: 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 121 of 150 in Extreme Sudoku 1
Difficulty
Expert 6 (expert and beyond), from the final, hardest third of the book
Key technique
Nice Loops/AICs
Hard steps
25 of 51 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 (×8), 2-String Kite (×2), ALS-XZ, Cell Forcing Chains, Sue de Coq, W-Wing, WXYZ-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 (24 of 25)
  1. Step 5 · 2-String Kite advanced
    Rules out 4 from R8C7.
  2. Step 6 · Nice Loops/AICs expert
    Rules out 6 from R7C2.
  3. Step 7 · ALS-XZ expert
    Rules out 6 from R8C8.
  4. Step 8 · Nice Loops/AICs expert
    Rules out 6 from R8C7.
  5. Step 9 · Cell Forcing Chains expert
    Rules out 8 from R1C3.
  6. Step 12 · Nice Loops/AICs expert
    Rules out 8 from R8C4.
  7. Step 13 · Nice Loops/AICs expert
    Rules out 2 from R6C6.
  8. Step 17 · Sue de Coq expert
    Rules out 2 from R5C2; 5 from R5C2; 6 from R6C8, R6C9.
  9. Step 18 · WXYZ-Wing expert
    Rules out 6 from R6C1.
  10. Step 19 · Nice Loops/AICs expert
    Rules out 4 from R8C9.
  11. Step 20 · Nice Loops/AICs expert
    Rules out 4 from R8C8.
  12. Step 23 · Nice Loops/AICs expert
    Rules out 8 from R7C3.
  13. Step 25 · W-Wing advanced
    Rules out 7 from R3C2.
  14. Step 26 · Nice Loops/AICs expert
    Rules out 7 from R3C7.
  15. Step 27 · Nice Loops/AICs expert
    Rules out 7 from R3C8.
  16. Step 28 · Nice Loops/AICs expert
    Rules out 5 from R7C7.
  17. Step 33 · 2-String Kite advanced
    Rules out 6 from R4C8.
  18. Step 37 · XY-Chain expert
    Rules out 6 from R1C8.
  19. Step 38 · XY-Chain expert
    Rules out 1 from R1C1, R3C1, R8C2.
  20. Step 41 · XY-Chain expert
    Rules out 4 from R1C7, R3C1.
  21. Step 43 · XY-Chain expert
    Rules out 6 from R1C6.
  22. Step 44 · XY-Chain expert
    Rules out 7 from R1C7.
  23. Step 45 · XY-Chain expert
    Rules out 1 from R9C8.
  24. Step 46 · XY-Chain expert
    Rules out 2 from R6C2.

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.