Did You Figure It Out?

Answer...

18

Solution:

Let

* x denote the number of days we jogged in the morning and stayed at home in the evening;
* y denote the number of days we played tennis in the evening and did nothing in the morning; and
* z denote the number of days we neither jogged nor played tennis.

Then,

y + z = number of mornings we did nothing = 9
x + z = number of evenings we stayed at home = 14
x + y = number of days we jogged or played tennis = 13

Adding the above three equations and dividing both sides by 2 gives

x + y + z = 18

Since there are only three types of days, the total number of days I stayed with my cousin is their sum, i.e., 18.