**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 = 15

*x* +

*z* = number of evenings we stayed at home = 17

*x* +

*y* = number of days we jogged or played tennis = 16

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

*x* +

*y* +

*z* = 24

Since there are only three types of days, the total number of days I stayed with my cousin is their sum, i.e., 24.

**Food for thought:**
Can you solve this puzzle using a Venn diagram with two intersecting sets? Could the two sets be "days we did nothing in the morning" and "days we stayed at home in the evening"?