Kakuro

Kakuro or Kakkuro or Kakoro (Japanese: カックロ) is a kind of logic puzzle that is often referred to as a mathematical transliteration of the crossword.

The popularity of Kakuro in Japan is immense, second only to Sudoku among Nikoli's famed logic-puzzle offerings.

[2] The canonical Kakuro puzzle is played in a grid of filled and barred cells, "black" and "white" respectively.

It is that lack of duplication that makes creating Kakuro puzzles with unique solutions possible.

At least one publisher[3] includes the constraint that a given combination of numbers can only be used once in each grid, but still markets the puzzles as plain Kakuro.

The solution space can be reduced by resolving allowable intersections of horizontal and vertical sums, or by considering necessary or missing values.

When solving longer sums there are additional ways to find clues to locating the correct digits.

Harder ones require the use of various types of chain patterns, the same kinds as appear in Sudoku (see Pattern-Based Constraint Satisfaction and Logic Puzzles[5]).

[7] There are two kinds of mathematical symmetry readily identifiable in Kakuro puzzles: minimum and maximum constraints are duals, as are missing and required values.

Kakuro remained the most popular logic puzzle in Japanese printed press until 1992, when Sudoku took the top spot.