EXTREMEPUZZLE BOOKS

Extreme Killer Sudoku 1, puzzle 89: 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
Killer sudoku, number 89 of 150 in Extreme Killer Sudoku 1
Difficulty
Expert 3 (expert and beyond), from the middle third of the book
Key technique
Finned Fish
Hard steps
9 of 73 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: Finned Fish

An X-Wing or Swordfish with one extra candidate (the fin). Cells that are in the fish pattern and also see the fin lose the digit.

Other advanced and expert techniques in this solve: Advanced Innies (3+ sectors) (×3), Empty Rectangle, Forcing Chains, Multi-Sector Locking, Remote Pairs, XYZ-Wing.

Every move above the basics is listed on the killer sudoku techniques page, each with a one-sentence explanation and worked examples from the books.

The hard steps, in text (9)
  1. Step 9 · XYZ-Wing advanced
    Rules out 7 from R4C2, R5C2.
  2. Step 11 · Multi-Sector Locking advanced
    Rules out 3 from R5C2, R5C3.
  3. Step 13 · Advanced Innies (3+ sectors) advanced
    Rules out 1 from R1C4, R6C4; 5 from R1C4, R6C4, R7C8; 2 from R6C4.
  4. Step 15 · Finned Fish expert
    Rules out 9 from R1C7, R1C8, R2C7.
  5. Step 16 · Forcing Chains expert
    Rules out 9 from R1C1, R1C2, R2C1, R2C2 and 8 more; 2 from R2C2, R3C2, R9C1; 7 from R6C2, R9C1.
  6. Step 20 · Remote Pairs expert
    Rules out 6 from R4C2, R5C2, R8C3, R9C3; 7 from R8C3, R9C3.
  7. Step 40 · Advanced Innies (3+ sectors) advanced
    Places 9 in R7C8 and rules out 7 from R3C6, R4C6; 4 from R5C6, R8C6, R9C6; 9 from R5C8, R7C4, R7C7, R8C7 and 1 more.
  8. Step 55 · Empty Rectangle advanced
    Rules out 1 from R1C7.
  9. Step 56 · Advanced Innies (3+ sectors) advanced
    Rules out 7 from R1C4; 5 from R5C6, R6C1, R6C5, R6C9 and 1 more; 3 from R6C1, R6C4, R6C5.

The book

No starting digits at all: just cages and their totals. Sudoku rules, plus arithmetic, plus a lot of nerve.

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