Kakuro
Kakuro is a number puzzle laid out like a crossword in which each run of white squares must add up to the total printed in the clue square at its head, using only the digits 1 to 9 and never repeating a digit within the same run.
A clue square is split by a diagonal line. The number written above and to the right is the total for the run of squares heading across to the right; the number below and to the left is the total for the run heading down. Every white square therefore belongs to one across run and one down run, and its digit has to satisfy both.
The way in is combinatorics rather than addition. Some totals can be reached only one way for a given run length: three across two squares must be 1 and 2 in some order, and sixteen across two must be 7 and 9. Seasoned solvers memorise these forced combinations, then use the overlap between an across run's options and a down run's options to pin a single square.
Nikoli published the puzzle in Japan and the name is a contraction of the Japanese for addition cross. In English-language magazines it has also been sold as Cross Sums.