EXTREMEPUZZLE BOOKS

Extreme Sudoku 1, puzzle 123: 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 123 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
27 of 54 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), ALS-XZ (×3), 2-String Kite (×2), Empty Rectangle (×2), XY-Wing (×2), Cell Forcing Chains, Finned Fish, Sue de Coq, X-Wing/Swordfish.

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 27)
  1. Step 6 · 2-String Kite advanced
    Rules out 3 from R9C5.
  2. Step 7 · X-Wing/Swordfish advanced
    Rules out 3 from R7C1, R7C4.
  3. Step 8 · ALS-XZ expert
    Rules out 9 from R4C5.
  4. Step 9 · Nice Loops/AICs expert
    Rules out 7 from R4C4.
  5. Step 10 · Nice Loops/AICs expert
    Rules out 5 from R7C9.
  6. Step 11 · Cell Forcing Chains expert
    Rules out 2 from R3C3.
  7. Step 13 · Empty Rectangle advanced
    Rules out 2 from R4C4.
  8. Step 14 · ALS-XZ expert
    Rules out 8 from R8C2.
  9. Step 15 · Nice Loops/AICs expert
    Rules out 8 from R7C8.
  10. Step 16 · Sue de Coq expert
    Rules out 8 from R9C1; 9 from R9C1, R9C3, R9C6.
  11. Step 19 · Nice Loops/AICs expert
    Rules out 9 from R8C6.
  12. Step 20 · Nice Loops/AICs expert
    Rules out 7 from R1C5.
  13. Step 21 · Nice Loops/AICs expert
    Rules out 2 from R4C1.
  14. Step 22 · ALS-XZ expert
    Rules out 9 from R4C3.
  15. Step 23 · Empty Rectangle advanced
    Rules out 9 from R1C6.
  16. Step 25 · Nice Loops/AICs expert
    Rules out 9 from R8C1.
  17. Step 26 · Nice Loops/AICs expert
    Rules out 7 from R4C5.
  18. Step 27 · Nice Loops/AICs expert
    Rules out 7 from R6C1.
  19. Step 28 · Nice Loops/AICs expert
    Rules out 7 from R6C2.
  20. Step 31 · 2-String Kite advanced
    Rules out 7 from R8C1.
  21. Step 32 · XY-Wing advanced
    Rules out 9 from R7C2, R8C2.
  22. Step 33 · Finned Fish expert
    Rules out 7 from R8C3.
  23. Step 35 · XY-Chain expert
    Rules out 6 from R1C2.
  24. Step 36 · XY-Chain expert
    Rules out 7 from R1C3.

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.