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

Are they implying that interaction (I) between children (c) is a quadratic function ????

then

I(c)= (c-1)^2

so I(8) = 7^2 = 49

(look like a text-book editor's feeble attempt to "make mathematics real" )

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 6 interactions.
If there are 3 children, there can be 15 interactions.
If there are 4 children, there can be 27 interactions.

How many interactions will there be for 7 children?

60

81

105

108

105

To find the number of interactions for 8 children, we can observe a pattern in the given examples. Let's break down the interactions for each scenario:

1 child: 0 interactions
2 children: 1 interaction
3 children: 4 interactions
4 children: 9 interactions

By examining the pattern, we can notice that the number of interactions is increasing based on the square of the number of children.

To calculate the number of interactions for 8 children, we can use this pattern:

Number of interactions = (Number of children)^2

Plugging in the value for 8 children:

Number of interactions = 8^2
= 64

Therefore, there will be 64 interactions for 8 children on the playground.