At a new years eve party, each person in the room kissed every person in the room. If there were 190 kisses total, how many people were at the party?
by 
hales123
ANSWERS: 10
-
20 I think
-
15? I haven't taken any math classes in a while, I should be able to figure this out, but I can't
-
I am going with 13 people here.
-
it's impossible because the square root of 190 which is what you need to do to figure out the answer is 13.78
-
20 people who each kissed 19. Half are shared and count as one. 20 times 19 equals 380 divided by two equals 190?
-
It's 20. I don't have a mathematical formula for you though I just drew it out on paper.
-
19 people :)
-
The pattern follows the triangular rule: n(n-1)/2 People Kisses 1 0 2 1 3 3 4 6 190 = n(n-1)/2 380 = n(n-1) 0 = n^2 - n - 380 n = (-b +/- sqrt(b^2 - 4ac))/2a n = (1 +/- sqrt(1 + 1520))/2 n = (1 +/- sqrt(1521))/2 n = (1 +/- 39)/2 n = 40/2 & = -38/2 n= 20 & = -19 You cannot have a negative number of people, hence n = 20!
-
Another complete the square puzzle. Suppose n people. Each person kisses n-1 people. But there are two people involved in each kiss, so the total number of kisses is n*(n-1)/2. n * (n-1) / 2 = 190 n^2 - n = 380 (n - (1/2))^2 would be n^2 - n + (1/4), so (n - (1/2))^2 - (1/4) = 380 (n - (1/2))^2 = 380 + 1/4 = 1521/4 n - (1/2) = +/- sqrt(1521/4) = +/- 39/2 n = 1/2 + 39/2 n = 40/2 n = 20
-
THAT WOULD DEPEND UPON WHOM YOU ARE SPEAKING WITH AT THE MOMENT!!! I'LL NEVER TELL...
RELATED QUESTIONS
Copyright 2023, Wired Ivy, LLC