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# Cross Sums

A logic puzzle sometimes called Kakuro.

The Cross Sums is a very common type of logic puzzle that is often referred to as a mathematical transliteration of the crossword. In principle, "Cross Sums" puzzles are integer programming problems, and can be solved using matrix techniques, although they are typically solved by hand. "Cross Sums" are regular features in most, if not all, math-and-logic puzzle publications in the United States; Dell Magazines uses the "Cross Sums" name, which was formerly unique to them but is now in common use among various publishers (although some other names, such as "Cross Addition", are still used). In Japan, where the puzzle is called Kakro, its popularity is immense, second only to "Sudoku" among Nikoli's famed logic-puzzle offerings; in an international tapdance, Kappa reprints Nikoli "Kakro" in the United States, in "GAMES Magazine" under the name "Cross Sums". "The Guardian" in Britain began printing the puzzle under the name Kakuro in September 2005; since then many other British papers have followed suit and now also print daily puzzles.

**Standard play and terminology**

The canonical "Cross Sums" puzzle is played in a grid of filled and empty cells - "black" and "white", respectively - usually 16�16 in size but 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 "Cross Sums" with unique solutions possible.

Source: Wikipedia

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