Killer Sums is sudoku without any starting digits. Instead the grid is cut into dotted cages, and each cage shows the total of the digits inside it. Those totals, together with the usual row, column and box rules, are enough to pin down every cell. Every puzzle here is generated fresh and checked by a solver so that it has exactly one answer.
How to play
The rules.
- Every row contains each digit once (1 to 6 on the small grid, 1 to 9 on the large one).
- Every column contains each digit once.
- Every box (the areas marked by thick lines: 2×3 on the small grid, 3×3 on the large) contains each digit once.
- The digits inside a dotted cage add up to the small number in its top-left corner, and a digit never repeats inside a cage.
Entering digits. Tap a cell, then tap a digit on the panel below the grid; Erase clears it. On a keyboard, type the digit, use Backspace to clear, and move between cells with the arrow keys. A cage with a single cell simply tells you its digit.
Mistakes and help. Two equal digits in a row, column, box or cage are highlighted, and so is a complete cage whose total is wrong. Hint fixes a wrong digit if you have one, otherwise it fills one correct cell. Undo takes back your last change. The timer and the number of hints you used appear when you finish.
Difficulty. Choose under Difficulty at the top; New puzzle creates another grid at that size.
| Level | Grid | Cages |
|---|---|---|
| Easy | 6 × 6, 2×3 boxes | up to 3 cells, many single cells |
| Medium | 9 × 9, 3×3 boxes | up to 4 cells |
| Hard | 9 × 9, 3×3 boxes | up to 5 cells, few single cells |
Strategy
Start with the extremes. A two-cell cage totalling 3 must be 1 and 2; a total of 17 must be 8 and 9. Three cells adding to 6 are 1, 2, 3; three cells adding to 24 are 7, 8, 9. Write those combinations down first.
Use the 45 rule. On the 9×9 grid every row, column and box adds up to 45 (21 on the 6×6 grid). If a box is covered by cages except for one cell, that cell is 45 minus the cage totals inside the box. A cage that sticks one cell out of a box tells you that cell the same way.
No repeats in a cage. A cage totalling 10 over three cells cannot use 5 twice, so it is 1+4+5, 2+3+5 or 1+2+7, never 5+5+0. The no-repeat rule often rules out a combination that the row rule alone would allow.
Count the candidates. Once a cage has one open cell, its digit is the remaining difference. When two cells of a cage are in the same row, the row rule and the cage rule work together.
If you enjoy Killer Sums, try Light Up or Mahjong Solitaire next.
