How many “clinks” will there be?

Question

At a party, someone proposes a toast. Each of the 20 people in the room wants to “clink” glasses with everyone else. How many “clinks” will there be? (There is exactly one “clink” for every pair of people).

Answer 1

20 for the first

19 for the second

18 for the third

17 for the fourth

....

 

20+19+18+ ... + 3 +2 +1 =

 

20*21/2 = 210

 

The formula for the sum of the first N integers is N(N+1)/2

 

with N=20.