Proposed by Peter Nightingale

Killer Sudoku is a puzzle played on a $\{9\times 9\}$ grid containing 81 cells. The cells are filled in with numbers from the set $\{1\ldots 9\}$. Each row and column must contain all numbers $\{1\ldots 9\}$. Each of the 9 non-overlapping $3\times 3$ subsquares (named boxes) must also contain all numbers $\{1\ldots 9\}$.

Each Killer Sudoku puzzle has a set of cages. A cage is a set of contiguous cells and a total; the numbers in the cells must add up to the total. Also, the cells in a cage cannot contain the same number more than once. The cages do not overlap, and they cover all cells. Cages typically contain two to four cells. Typically a Killer Sudoku puzzle will have exactly one solution.

An example Killer Sudoku puzzle is shown below. Each cage is shown as an area of one colour.

Killer Sudoku Puzzle
A Killer Sudoku Puzzle (public domain image from Wikipedia)

The solution of the above puzzle is shown below.

Killer Sudoku Puzzle Solution
A Killer Sudoku Puzzle Solution (public domain image from Wikipedia)

Generalisation to $n \times n$ grids

There is a straightforward generalisation of Killer Sudoku. For any $n$ that has an integer square root, we have an $n \times n$ grid and each cell takes any value in $\{1\ldots n\}$. In a solution each row and column contains all numbers $\{1\ldots n\}$, and the $n$ non-overlapping $\sqrt{n} \times \sqrt{n}$ boxes also contain all numbers $\{1\ldots n\}$. Cages function in the same way in the generalised problem as in the $\{9\times 9\}$ problem.