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 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?

135

84

93

108

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 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? 

 135 

 84 

 93 

 108

anonymous · Answer

Oh & I know the answer is not 93

shubhamsrg · Answer

nth child corresponds to 3n(n-1)/2 interactions

anonymous · Answer

how do I fill out the formula?

shubhamsrg · Answer

just substitute n=9 if you want to know no. of interactions for 9th child

anonymous · Answer

wooooow! Thank you soo much! I think I understand a little bit better now!

shubhamsrg · Answer

glad in case I could help