EXTREMEPUZZLE BOOKS

Extreme Killer Sudoku 1, puzzle 137: 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 137 of 150 in Extreme Killer Sudoku 1
Difficulty
Expert 3 (expert and beyond), from the final, hardest third of the book
Key technique
Forcing Chains
Hard steps
11 of 97 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: Multi-Sector Locking (×5), XY-Wing (×2), Advanced Innies (3+ sectors), Coloring/Multi-coloring, 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 (11)
  1. Step 15 · Multi-Sector Locking advanced
    Rules out 1 from R1C1, R2C1; 2 from R8C4.
  2. Step 18 · Advanced Innies (3+ sectors) advanced
    Places 3 in R9C4, 6 in R9C5 and rules out 3 from R1C4, R2C4, R3C4; 6 from R1C5, R2C5, R3C5, R4C5 and 2 more.
  3. Step 20 · Forcing Chains expert
    Rules out 1 from R6C8.
  4. Step 37 · XY-Wing advanced
    Rules out 4 from R7C3.
  5. Step 38 · XY-Wing advanced
    Rules out 1 from R7C3.
  6. Step 40 · Multi-Sector Locking advanced
    Rules out 9 from R1C3, R2C3, R5C2, R6C2 and 1 more; 6 from R4C3, R5C3.
  7. Step 69 · Multi-Sector Locking advanced
    Rules out 2 from R2C6.
  8. Step 70 · Remote Pairs expert
    Rules out 9 from R3C2.
  9. Step 72 · Multi-Sector Locking advanced
    Rules out 9 from R2C8, R2C9.
  10. Step 73 · Coloring/Multi-coloring expert
    Rules out 1 from R1C7.
  11. Step 79 · Multi-Sector Locking advanced
    Rules out 1 from R1C5, R2C7.

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.