I’ve been doing Cross-Sum puzzles for many years, but now that it’s called Kakuro (abbreviation of Japanese kasan kurosu: addition cross), it seems somehow new. Certainly the Puzzle book publishers think so. Where there was previously only a section in a crossword puzzle book there is now entire puzzle books devoted to Kakuro.
In solving these kinds of puzzles it may be useful as a solving aid to know about minimum and maximum values for the length of each clue number and a way of dealing with missing and required values in partial sums. One such way is to map missing values to 0 and required values to 1, to get a bit-wise string of bits for which bit-wise logical operations can be performed: and, or, exclusive or, not.