EXTREMEPUZZLE BOOKS

Extreme Killer Sudoku 3, puzzle 78: 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 78 of 150 in Extreme Killer Sudoku 3
Difficulty
Expert 2 (expert and beyond), from the middle third of the book
Key technique
Forcing Chains
Hard steps
11 of 94 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: Forcing Chains

Try each candidate of one cell in turn. Every choice leads to the same result, so that result must be true.

Other advanced and expert techniques in this solve: Empty Rectangle (×3), Advanced Innies (3+ sectors) (×2), Skyscraper (×2), Multi-Sector Locking, Remote Pairs, XY-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 (11)
  1. Step 10 · Empty Rectangle advanced
    Rules out 8 from R3C6.
  2. Step 11 · Empty Rectangle advanced
    Rules out 9 from R3C6.
  3. Step 12 · Multi-Sector Locking advanced
    Rules out 6 from R5C8, R6C8; 7 from R6C5, R6C6, R6C7.
  4. Step 13 · Advanced Innies (3+ sectors) advanced
    Places 8 in R1C4, 6 in R1C5 and rules out 6 from R1C1, R1C2, R1C3, R1C6 and 10 more; 8 from R1C1, R1C6, R1C7, R2C5 and 10 more; 9 from R6C1, R6C8.
  5. Step 20 · Empty Rectangle advanced
    Rules out 8 from R5C1.
  6. Step 21 · Forcing Chains expert
    Rules out 1 from R1C6; 2 from R1C6; 3 from R1C6.
  7. Step 42 · Advanced Innies (3+ sectors) advanced
    Rules out 2 from R5C8; 1 from R5C9; 5 from R6C3.
  8. Step 44 · Remote Pairs expert
    Rules out 4 from R5C8.
  9. Step 55 · Skyscraper advanced
    Rules out 1 from R6C7.
  10. Step 69 · XY-Wing advanced
    Rules out 1 from R3C7.
  11. Step 74 · Skyscraper advanced
    Rules out 4 from R2C2.

The book

Volume three: 150 new killers, none repeated from books 1 or 2. No starting digits, just cages and their totals, 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.

On Amazon from 15 Dec About the book

Try a free sample puzzle (PDF) · prints on A4 or US Letter

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