Kakuro is one of the two superstars of this puzzle genre, and like sudoku it was actually invented in the United States.
According to Will Shortz, the first "cross sums" puzzle appeared in 1966 in a Dell puzzle magazine. Around 1980, it was spotted by McKee Kaji, founder of Nikoli, who brought the puzzle to Japan. It came back to the US in the aftermath of the sudoku craze.
Puzzle and Goal
An unsolved puzzle consists of a rectangular grid resembling a crossword, with some black cells containing numbers.
The goal is to fill the (non-black) cells with numerals from 1 to 9.
The solved grid must satisfy the following conditions:
Considering the grid as a crossword puzzle, the sum of the digits in any entry matches that of the clue at the right or the top of the entry.
No digit can appear more than once in any entry.
The most common variants are Cross Products, where the clues are the products rather than the sums, and puzzles where numerals are restricted to some range other than 1 to 9.
In the variant Sukrokuro, walls between cells either have a circle or not. The circle indicates that these cells contain consecutive numbers; consecutive numbers cannot appear in neighboring cells otherwise.
Cross Addition; Cross Products; Cross Sums; Kasan Kurosu; Kreuzsumme; Sukrokuro; Zahlenschwede