SOLO-009 · Killer Sudoku
EXPERTCaptive Sums
Complete the grid completely. Only one solution respects all constraints.
Materials: Pencil and gum; no commercial material.
Rules you need
- Fill in the 81 boxes with numbers from 1 to 9. Each row and column contains each of the nine digits exactly once.
- The coordinates L1C1 to L9C9 are read from the top left corner. No calculation is made on the coordinates numbers.
- Each of the nine blocks of 3 × 3 also contains numbers 1 to 9 without repetition.
- Each dotted cage carries a total. The numbers of the cage have this sum and are all different; this prohibition also applies between two cells of the cage that do not share a line, column or block. The few pre-filled figures are part of the problem.
The puzzle
The empty boxes are to be completed. The given numbers are fixed. The answer and proof are on another page.
| L / C | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 208 | 13 | 12 | 22 | |||||
| 2 | 18 | 24 | 11 | ||||||
| 3 | 16 | 17 | |||||||
| 4 | 124 | 16 | 21 | 3 | 14 | ||||
| 5 | 15 | 13 | |||||||
| 6 | 10 | 18 | |||||||
| 7 | 15 | 8 | 18 | 12 | 17 | 14 | |||
| 8 | 19 | 9 | |||||||
| 9 | 3 | 15 |
Thick stroke: region. Dotted inside the cells: cage and its total. A tint on a diagonal reminds the diagonal constraint, if it applies.
Exact list of cages (coordinates and totals)
- Cage 1: L1C1, L1C2, L1C3, L2C1; total 20.
- Cage 2: L1C4, L1C5, L1C6; total 13.
- Cage 3: L1C7, L1C8; total 12.
- Cage 4: L1C9, L2C8, L2C9, L3C8; total 22.
- Cage 5: L2C2, L3C1, L3C2, L3C3; total 18.
- Cage 6: L2C3, L2C4, L3C4; total 24.
- Cage 7: L2C5, L2C6, L2C7; total 11.
- Cage 8: L3C5, L3C6, L3C7, L4C7; total 16.
- Cage 9: L3C9, L4C9, L5C9; total 17.
- Cage 10: L4C1, L4C2, L5C2; total 12.
- Cage 11: L4C3, L4C4, L5C3, L5C4; total 16.
- Cage 12: L4C5, L5C5, L5C6; total 21.
- Cage 13: L4C6; total 3.
- Cage 14: L4C8, L5C8, L6C8, L6C9; total 14.
- Cage 15: L5C1, L6C1; total 15.
- Cage 16: L5C7, L6C7; total 13.
- Cage 17: L6C2, L6C3, L6C4; total 10.
- Cage 18: L6C5, L6C6, L7C5; total 18.
- Cage 19: L7C1, L7C2; total 15.
- Cage 20: L7C3, L8C3; total 8.
- Cage 21: L7C4, L8C4, L9C4, L9C5; total 18.
- Cage 22: L7C6, L8C6; total 12.
- Cage 23: L7C7, L7C8, L8C7, L8C8; total 17.
- Cage 24: L7C9, L8C9, L9C9; total 14.
- Cage 25: L8C1, L8C2, L9C2, L9C3; total 19.
- Cage 26: L8C5; total 9.
- Cage 27: L9C1; total 3.
- Cage 28: L9C6, L9C7, L9C8; total 15.
Your workspace
Write down your assumptions separately from deductions you have proved.