Can you give me a hand?

Question

At a family reunion, everyone shakes everyone else's hand once. Not one person shakes someones else's hand twice. If a total of 190 handshakes take place, how many people were at the reunion?

Answer 1

n(n-1)/2 =190
n2 - n - 380 = 0
D =1 - 4 x -380 = not a square of an integer
There is no solution since n must be an integer.

Th

Answer 2

I'm guessing this is a statistics problem and each person can shake more than one person's hand. If so, Jim C is right and you use the simple statistical combination equation for the number of possible pairs in a group: (n(n-1))/2 = 190. This reduces to the quadratic equation n^2-n-380=0. That can be solved by factoring it into (n+19)(n-20) = 0. The negative solution is discarded, making the answer 20.

Answer 3

HERE'S THE ANSWER.
IF EVERY MAN SHAKES HAND ONCE WITH EVERYONE THEN IT MEANS THEN AFTER THAT HE CAN BE DEDUCTED FROM COUNT. THEN ONE PERSON FROM THE LEFT OVER PEOPLE WILL SHAKE AND AND WHEN HE IS DONE HE WILL QUIT FROM COUNT AND SAME GOES TILL THE LAST NUMBER. HERE'S A CALCULATION:

THE TOTAL PEOPLE IN THE REUNION ARE 20.
BECAUSE (AS DESCRIBED ABOVE) WE WILL DEDUCT THE NYMBER OF MEN, ONE AT A TIME.
19+18+17+16+15+14+13+12+11+10+9+8+7+6+5+4+3+2+1+0 =190 handshakes.
first man will shake with 19 people and the last man, as he has shaked with everyone will be left alone.
SO THE TOTAL NUMBER OF PEOPLE ARE 20.
ITS 100% CORRECT.
THANK YOU!

Answer 4

190 * 2 = 380

Answer 5

the equation to solve is

n(n-1)/2 = 190

for n people there will be n(n-1)/2 handshakes.

so you have,

n^2 - n - 380 = 0.

Answer 6

{clapping}