At a birthday party, 13 children ate cake, 9 ate ice cream, 7 ate both cake and ice cream, and one c

At a birthday party, 13 children ate cake, 9 ate ice cream, 7 ate both cake and ice cream, and one child had neither cake nor ice cream. How many children were at the party?

We have one of three scenarios

1. A child ate cake (possibly ice-cream)
2. A child ate ice cream (possible cake)
3. A child ate neither

We have cake + ice cream + neither - both cake and ice cream.
We subtract both cake and ice cream to avoid duplicates

13 + 9 + 1 - 7 = 16 kids at the party