Question 606867: if a basketball team hi-fives each other and there is a total of 66 hi-fives, how many players on the team? what is the formula to solve this equation?
Found 2 solutions by scott8148, solver91311:
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! if n people high-five each other, then each person high-fives n-1 other people
BUT ... Tom high-fiving Bill is the same as Bill high-fiving Tom
so for n people, the number of high-fives is ___ [n(n-1)] / 2
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
Let's say there are  guys on the team. Since he can't high-five himself, the first guy is going to do  high-fives. The second guy is going to do just as many, but we have already counted one of them, namely the high-five the first guy already did with him, hence the second guy has  uncounted high-fives. Likewise the third guy has  , and so on.
So we have \ +\ (n\ -\ 2)\ +\ (n\ -\ 3)\ +\ \cdots\ +\ \left(n\ -\ (n\ -\ 1)\right)\ +\ (n\ -\ n))
which, if you turn it around, is nothing more than the sum of the integers from 1 to
Just for neatness sake, let's use  to represent , then
}{2}\ =\ 66)
Solve for and then add 1 to get
John
My calculator said it, I believe it, that settles it
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