EXTREMEPUZZLE BOOKS

Extreme Killer Sudoku 1, puzzle 15: 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 15 of 150 in Extreme Killer Sudoku 1
Difficulty
Expert 3 (expert and beyond), from the opening third of the book
Key technique
Coloring/Multi-coloring
Hard steps
10 of 83 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: Coloring/Multi-coloring

Following one digit’s strong links, cells get two colours: one colour is true and the other is false. A cell that sees both colours cannot hold the digit.

Other advanced and expert techniques in this solve: Multi-Sector Locking (×3), Advanced Innies (3+ sectors) (×2), Empty Rectangle (×2), Forcing Chains, Remote Pairs.

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 (10)
  1. Step 8 · Empty Rectangle advanced
    Rules out 8 from R6C8.
  2. Step 9 · Advanced Innies (3+ sectors) advanced
    Rules out 9 from R1C3, R1C4, R2C3, R2C4; 4 from R1C4, R2C4; 8 from R1C4, R2C4.
  3. Step 14 · Multi-Sector Locking advanced
    Rules out 8 from R2C7; 9 from R2C7.
  4. Step 15 · Coloring/Multi-coloring expert
    Rules out 9 from R3C8.
  5. Step 16 · Forcing Chains expert
    Rules out 9 from R6C6.
  6. Step 43 · Multi-Sector Locking advanced
    Rules out 2 from R1C3, R2C3.
  7. Step 44 · Advanced Innies (3+ sectors) advanced
    Rules out 7 from R1C3, R2C3; 5 from R1C4, R2C4, R6C5; 4 from R1C5, R2C5, R3C5.
  8. Step 55 · Empty Rectangle advanced
    Rules out 6 from R3C8.
  9. Step 56 · Multi-Sector Locking advanced
    Rules out 5 from R7C1.
  10. Step 58 · Remote Pairs expert
    Rules out 4 from R6C3; 7 from R6C3.

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.