Question 1059824: After winning the championship, all Dallas Maverick teammates hugs. Altogether there were 66 hugs. How many players were there?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Let x = number of players
A player cannot hug themself, so there are x-1 choices for any one player to hug.
There are x*(x-1) ways to have players hug assuming order mattered (eg: AB is different from BA)
However, player A hugging player B is the same as B hugging A. Order does not matter. This means we must correct for the double count by dividing by 2
The expression for the number of hugs is x*(x-1)/2
Set this equal to 66 and solve for x
x*(x-1)/2 = 66
2*x*(x-1)/2 = 66*2
x*(x-1) = 132
x^2 - x = 132
x^2 - x - 132 = 0
(x - 12)(x + 11) = 0
x - 12 = 0 or x + 11 = 0
x = 12 or x = -11
Toss out the negative number. Only x = 12 makes sense
So there are 12 players on the team.
|
|
|
