How many kisses do you get if every person in a room full of ten people kisses every other person once? The first person kisses 9 others, the second one kisses 8 others (having already kissed the first), the third kisses 7 others, and so on, with the 10th person not having any new person to kiss at all. So in total you get

9+8+7+ …. +2+1 = 45

kisses. You can also look at this another way. Every person kisses 9 others and there are 10 people, giving 10×9=90 kisses. But this counts every kiss twice, so we have to divide by 2 to get a total of

10×9/2=45 kisses.