Online games and puzzles

The canonical Kakuro puzzle is played in a grid of filled and empty cells — "black" and "white", respectively — usually 16×16 in size, but these dimensions can vary widely. Apart from the top row and leftmost column — which are entirely black — the grid, just like a crossword, is divided into "entries" — orthogonal lines of white cells — by the black cells. The black cells themselves — possibly barring those in a cluster — are not entirely solid but rather contain a diagonal slash from upper-left to lower-right and a number in one or both halves, such that each horizontal entry has a number in the black half-cell to its immediate left and each vertical entry has a number in the black half-cell immediately above it. These numbers, continuing the borrowed crossword terminology, are commonly called "clues".

The object of the puzzle is to insert a digit from 1 to 9 inclusive into each white cell such that the sum of the numbers in each entry matches the clue associated with it and that no digit is duplicated in any entry. It is that lack of duplication that makes creating Kakuro puzzles with unique solutions possible, and which means solving a Kakuro puzzle involves investigating combinations more, compared to Sudoku in which the focus is on permutations.

Some publishers prefer to print their Kakuro grids exactly like crossword grids, with no labeling in the black cells and instead numbering the entries, providing a separate list of the clues akin to a list of crossword clues. (This eliminates the row and column that are entirely black.) This is purely an issue of image and does not affect solving (at least, not beyond the degree of needing to look outside the grid to solve).

In discussing Kakuro puzzles and tactics, the typical shorthand for referring to an entry is "(clue, in numerals)-in-(number of cells in entry, spelled out)", such as "16-in-two" and "25-in-five". The exception is what would otherwise be called the "45-in-nine" — simply "45" is used, since the "-in-nine" is mathematically implied (nine cells is the longest possible entry, and since it cannot duplicate a digit it must consist of all the digits from 1 to 9 once). Curiously, "3-in-two", "4-in-two", "5-in-two", "43-in-eight", and "44-in-eight" are still frequently called as such, despite the "-in-two" and "-in-eight" being equally implied.

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