# 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?

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1. 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" )

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2. 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

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3. 105

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