If there is 1 child, there can be 0 interactions.

If there are 2 children, there can be 3 interactions.

If there are 3 children, there can be 9 interactions.

If there are 4 children, there can be 18 interactions.

How many interactions will there be for 9 children?

a. 135

b. 84

c. 93

d. 108

Find the differences:

3-0 = 3

9-3 = 6

18-9 = 9

The differences increase by the previous difference plus 3

So 5 kids would have 9+3 = 12 + 18 = 30 interactions.

6 kids: 30-18 = 12 + 3 = 15 + 30 = 45 interactions.

7 kids: 15+3 = 18 + 45 = 63 interactions.

8 kids: 18 + 3 = 21 + 63 = 84 interactions.

9 kids: 21+3 = 24 + 84 = 108 interactions.

The answer is d. 108