A crossword with digits: each run of white cells adds up to its clue, using 1–9 without repeats.
The full guide, with a worked example and common mistakes: How to play Kakuro.
The number in the upper-right is the total for the run going across; the one in the lower-left is the total for the run going down.
Yes — see the Kakuro combinations chart, which lists every total for runs of 2 to 9 cells and marks the ones with a single combination.
Build it in the Kakuro Solver: click cells to make them black, enter the clues, then solve step by step.
It needs some arithmetic and combination knowledge, but the logic is similar. Easy Kakuro is a good next step after Sudoku.
Nine cells, which must contain every digit 1–9 and so always totals 45.