EXTREMEPUZZLE BOOKS

Extreme Killer Sudoku 1, puzzle 128: 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 128 of 150 in Extreme Killer Sudoku 1
Difficulty
Expert 2 (expert and beyond), from the final, hardest third of the book
Key technique
Remote Pairs
Hard steps
7 of 86 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), Forcing Chains, 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 (7)
  1. Step 6 · Multi-Sector Locking advanced
    Rules out 9 from R4C4.
  2. Step 7 · Advanced Innies (3+ sectors) advanced
    Places 5 in R5C2, 2 in R6C2 and rules out 2 from R2C2, R3C2, R4C1, R4C2 and 13 more; 5 from R2C2, R3C2, R4C1, R4C2 and 11 more; 7 from R7C4, R7C5.
  3. Step 31 · Multi-Sector Locking advanced
    Rules out 1 from R4C1.
  4. Step 37 · Advanced Innies (3+ sectors) advanced
    Rules out 5 from R3C4; 7 from R3C4, R5C4; 1 from R7C4.
  5. Step 40 · Remote Pairs expert
    Rules out 3 from R1C3, R2C3, R3C3; 4 from R1C3, R2C3, R3C3.
  6. Step 47 · Forcing Chains expert
    Rules out 8 from R1C4.
  7. Step 62 · XY-Wing advanced
    Rules out 1 from R4C3.

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.