Question

In a group of children, each child gives a gift to every other child. If the number of gifts is 132, then find the number of children

Answer 1

Suppose there are n children.
Then gifts bought by a single child = n-1

Now, 1 child bought n-1 gifts.
So n children will bring n x (n-1) gifts = 132 (given)
Thus, n(n-1) = n²-n = 132 => n² - n - 132 = 0

=> n² - 12n + 11n - 132 = 0 => n ( n - 12) + 11 ( n - 12) = 0
=> ( n+11 ) ( n - 12 ) = 0 => n = -11 and n = 12

But no. of children in negative (n = -11) is not possible. Thus, n = 12 .