EXTREMEPUZZLE BOOKS

Extreme Killer Sudoku 1, puzzle 31: 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 31 of 150 in Extreme Killer Sudoku 1
Difficulty
Expert 3 (expert and beyond), from the opening third of the book
Key technique
Forcing Chains
Hard steps
10 of 88 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: Advanced Innies (3+ sectors) (×4), Multi-Sector Locking (×2), Coloring/Multi-coloring, Empty Rectangle, Finned Fish.

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 12 · Multi-Sector Locking advanced
    Rules out 8 from R1C9, R2C7, R2C8, R2C9 and 3 more.
  2. Step 16 · Advanced Innies (3+ sectors) advanced
    Rules out 9 from R4C3; 3 from R7C3, R8C3.
  3. Step 18 · Forcing Chains expert
    Rules out 5 from R1C1, R1C2, R1C7, R1C8; 9 from R1C1, R1C2, R2C4, R2C5 and 9 more; 6 from R1C6.
  4. Step 43 · Advanced Innies (3+ sectors) advanced
    Rules out 8 from R4C3, R7C3; 9 from R5C1, R5C3; 5 from R7C3, R8C3.
  5. Step 46 · Finned Fish expert
    Rules out 1 from R7C3.
  6. Step 48 · Advanced Innies (3+ sectors) advanced
    Rules out 9 from R8C3; 5 from R8C4.
  7. Step 50 · Empty Rectangle advanced
    Rules out 8 from R6C6.
  8. Step 51 · Advanced Innies (3+ sectors) advanced
    Rules out 4 from R7C3; 5 from R7C4.
  9. Step 60 · Coloring/Multi-coloring expert
    Rules out 9 from R6C1, R7C2.
  10. Step 64 · Multi-Sector Locking advanced
    Rules out 7 from R5C1, R6C1; 5 from R6C6, R8C6, R9C1, R9C2.

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.

Buy on Amazon US Buy on Amazon UK
Other Amazon stores
About the book

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

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