Problem 9 · Fifteen handshakes
$\binom{n}{2} = 15$: the classic handshake count.
Integer answer, at most 4 digitsA group of friends meet and greet each other so that everyone shakes hands with everyone else. If fifteen handshakes took place, how many friends are in the group?
Copa Cangur · SCM
Easy
Closed answer
Reasoned solution
Key idea: with $n$ friends there are $\binom{n}{2} = \dfrac{n(n-1)}{2}$ handshakes.
$$\frac{n(n-1)}{2} = 15 \;\Longrightarrow\; n(n-1) = 30 \;\Longrightarrow\; n = 6.$$
Answer: 6