Question

A playground is being designed where children can interact with their friends in certain combinations.

If there is 1 child, there can be 0 interactions.
If there are 2 children, there can be only 1 interaction.
If there are 3 children, there can be 4 interactions.
If there are 4 children, there can be 9 interactions.

How many interactions will there be for 8 children? (1 point)

A) 49
B) 64
C) 36
D) 40

*I'm clueless about this recursive stuff. I've been stuck on it for the past hour and a half. I need help!!*

Answer 1

1 4 and 9 look awefully similar to squared numbers

Answer 2

? What?

Answer 3

I think what he's saying is if you look at the pattern
1 : 0^2
2 : 1^2
3 : 2^2
4 : 3^2
So it looks like the pattern is #interactions = (#children - 1)^2.

Answer 4

okay....

Answer 5

You can also solve it by drawing a picture of what it would look like, but with 8 children, the crisscrossing lines would get to cluttered.
Just follow the pattern. (Or use the explicit formula I gave you).

Answer 6

Thank you!