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?

49

64

36

40

Answer 1

look for a pattern in 0,1,4,9

if you know the squares you will see the pattern. If you don't, one strategy is find the differences between the numbers
0 1 4 9
1 3 5
maybe you see the pattern in the 2nd row (which we got by finding the differences in the first row). If you don't see a pattern, find the differences in the 2nd row
1 3 5
2 2

Now it's clear. the third row will be 2's
meaning the 2nd row is going up by 2
Here are the 2nd and 3rd rows, for a few more entries:
1 3 5 7 9
2 2 2 2

now we can find the first row:
0 1 4 9 x y
1 3 5 7 9

add the difference of 7 to 9 to find x

Answer 2

Very interesting, didn't think of searching for a pattern in the differences

Answer 3

of course that is the slow way, because you have to figure out the number for
8 children
1 2 3 4 5 6 7 8
0 1 4 9 x y z a
1 3 5 7 9 11 13

Answer 4

the fast way is to notice the pattern is (n-1)^2
where n is the # of children

Answer 5

So (8-1)^2?

Answer 6

Which would equal 49 if I'm not mistaken?

Answer 7

yes. if we do it the long way
it should be
9+
7 + 9 + 11 + 13
which adds up to 9+ 40= 49

Answer 8

Ah I see, thank you for the help phi :)

Answer 9

I have one more that is semi similar if you have the time, I'll be posting it shortly