Question 1059824
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.