Fifteen people from different places come together for a family reunion. Each one of them had two gifts each for every other person. When the gifts were exchanged they hugged each other. What is the difference between the number of hugs and the number of gifts exchanged?

We have $15$ people at a reunion. Each person brought $2$ gifts for every other person, and when they exchanged gifts, they hugged each other.

A hug involves $2$ people, and when Person A hugs Person B, that's the same hug as Person B hugging Person A. So we pick $2$ people from $15$ and divide by $2$ to avoid double counting:

$\text{Number of hugs} = \dfrac{15 \times 14}{2} = 105$

Each person gave $2$ gifts to every other person. Since each person has $14$ other people to give to:

$\text{Number of gifts} = 15 \times 14 \times 2 = 420$

We don't divide by $2$ here because giving is one-directional — if A gives $2$ gifts to B and B gives $2$ gifts to A, those are $4$ separate gifts.

$\text{Difference} = 420 - 105 = \boxed{315}$