chain patterns, the same kinds as appear in Sudoku (see Pattern-Based Constraint Satisfaction and Logic Puzzles). Mathematics of Kakuro Mathematically, Kakuro puzzles can be represented as integer programming problems, and are NP-complete. See also Yato and Seta, 2004. There are two kinds of mathematical symmetry readily identifiable in Kakuro puzzles: minimum and maximum constraints are duals, as are missing and required values. All sum combinations can be represented using a bitmapped representation. This representation is useful for determining missing and required values using bitwise logic operations. Popularity Kakuro puzzles appear in nearly 100 Japanese magazines and newspapers. Kakuro remained the most popular logic puzzle in Japanese printed press until 1992, when Sudoku took the top spot. In the UK, they first appeared in The Guardian, with The Telegraph and the Daily Mail following. See also Killer Sudoku, a variant of Sudoku which is solved using similar techniques. References External links The New Grid on the Block: The Guardian newspaper's introduction to Kakuro IAENG report on Kakuro Solve Kakuro puzzles online Logic puzzles NP-complete problems 1966 introductions