Kakuro is an entertaining puzzle for two reasons: it makes you think and then again, it makes you think. Now I know what you're thinking – she's gone bonkers! But there's more than one way to look at things…
First of all, Kakuro makes you think numerically: give someone a simple problem (for example, 1+2) and they can solve it comfortably (3, in case you're wondering). Give the same person a more difficult problem like 1+2+3+4+5+6+7+8+9 and they might make a grab for the calculator and hope that their fingers don't slip while tapping in all those numbers. Remove the calculator option and it's likely that they'll break down the problem into smaller parts: for example, 1+9, 2+8, 3+7, 4+6, plus 5 equals, wait for it, 45. This is the right way to approach a Kakuro puzzle: reduce the sums to a manageable size.
A Kakuro also makes you think logically. Each component comes with a limited number of possible options and, sometimes, an even smaller choice of where to put the answers. For example, a two-cell 14-sum could be filled with either a 5 and a 9 or a 6 and an 8; but only the 5 and 9 can cross with a four-cell 11-sum (1,2,3,5).
A Kakuro will have you whizzing between numerical and logical thinking until it becomes second nature; it's one of the great pleasures to be had from solving this puzzle.