EXTREMEPUZZLE BOOKS

Extreme Killer Sudoku 1, puzzle 114: 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 114 of 150 in Extreme Killer Sudoku 1
Difficulty
Expert 3 (expert and beyond), from the final, hardest third of the book
Key technique
Remote Pairs
Hard steps
9 of 98 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: Remote Pairs

A chain of cells that all hold the same pair alternates between the two digits. Cells that see both ends of an odd-length link cannot hold either digit.

Other advanced and expert techniques in this solve: Advanced Innies (3+ sectors) (×2), Multi-Sector Locking (×2), Skyscraper (×2), Coloring/Multi-coloring, Forcing Chains.

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 5 · Multi-Sector Locking advanced
    Rules out 1 from R5C9, R6C9, R7C9, R8C9; 2 from R5C9, R7C9, R8C9, R9C9.
  2. Step 8 · Advanced Innies (3+ sectors) advanced
    Places 4 in R6C9, 8 in R7C1 and rules out 8 from R1C1, R2C1, R3C1, R6C1 and 13 more; 4 from R1C9, R2C9, R3C9, R4C7 and 13 more; 5 from R5C8, R5C9.
  3. Step 26 · Skyscraper advanced
    Rules out 3 from R3C3.
  4. Step 27 · Multi-Sector Locking advanced
    Rules out 4 from R3C5; 9 from R3C5.
  5. Step 28 · Advanced Innies (3+ sectors) advanced
    Rules out 1 from R5C1, R5C2, R5C5; 6 from R5C5; 9 from R5C5.
  6. Step 36 · Skyscraper advanced
    Rules out 1 from R3C3.
  7. Step 37 · Remote Pairs expert
    Rules out 4 from R3C2; 6 from R3C2.
  8. Step 38 · Coloring/Multi-coloring expert
    Rules out 1 from R8C6.
  9. Step 82 · Forcing Chains expert
    Rules out 5 from R1C4.

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.